C h a p t e r
1 :
I n v e s t i n g
Note:
Answers
obtained
I the technology
I r-nson 1 1
.':
F i n a n c i a l
-
M a t h e m a t i c s ;
P i s $ 1 0 0 0 ; r i s 6 % o r 0 . 0 6 ; f is 5
4 = 1000(1 + ( 0 . 0 6 K 5 ) )
A = 1300
M o n e y
in these
used.
exercises
may
vary
T h e f u t u r e v a l u e is $ 1 3 0 0 ,
S i m p l e I n t e r e s t , p a c j e 14
CA
0 0 0 ; r is 3 . 5 % o r 0 . 0 3 5 ; t is 8
)0(1 + (0.035K8))
)0
n - ' - i ' j h i r e value .
/'(I
+rt)
e v a l u e is $ 3 8 4 0 0 .
Pfi + rt)
h i A-
P ( 1 + rt)
"i.idOO; r i s 5 % o r 0 , 0 5 ; f is 5
^000(1 + (0,05)(5))
0
•* i • .Q
I J /-
r '
-00; r i s 5 % o r 0 , 0 5 ; f is 6
••.'•'0(1 + ( 0 . 0 5 K 6 ) )
ru)0
300; r i s 1.25% o r 0 , 0 1 2 5 ' f is 4
)0(1 + ( 0 . 0 1 2 5 K 4 ) )
' •«"!>re v a l u e < . o r m a
3 v a l u e is $ 1 0 5 0 0 .
= P(1 + ff)
c)A
' n.h
i e the interest earned
F is $ 2 5 0 0 0 ; r is 0 . 5 % or 0 . 0 0 5 ' t is 2
1 3 1 2 . 5 0 ^ 1 0 0 0 = 312,50
•0(1 + (0.005K2))
0
Rate of return
= 3 1 2 ^
1000
Rate of r e t u m = 0,3125
i v a l u e is $ 2 5 2 5 0 .
•
T h e r a t e o f r e t u r n f o r o p t i o n A is 3 1 . 2 5 % .
-iOO; r i s 7 . 4 % o r 0 , 0 7 4 ; f is 2 0
0(1 + (0.074)(20))
* 0
/
2.a)A
A yields the greatest future value,
rt)
$4000; r i s 2 . 3 % or 0.023; l i s 5
1000(1 + ( 0 , 0 2 3 X 5 ) )
1460
.-f v a l u e is $ 2 9 7 6 0 .
= P+ Pn
'.'..11; P = $ 5 0 0 ( •
.
5
y e a r s , t h e f u t u r e v a l u e is $ 4 4 6 0
5000+(5000)(f)(5)
(',00 = 2 5 OOOf
I :>.')•}
0.06 = f
P is $ 4 0 0 0 ; f is 2 . 3 % o r 0 . 0 2 3 - f is 10
A = 4000(1 +(0.023)(10))
A = 4920
A f t e r 10 y e a r s , t h e f u t u r e v a l u e is $ 4 9 2 0 ,
6500 - 5000 + (5000)(r)(5)
1f/»(i
2*,000r
6
Ar. i . i t - , f r , t rate o f 6 % will a l l o w C a m to r e a c h his g o a l
P IS $ 5 0 0 0 : f is 6 % o r 0 . 0 6 ; t is 3
71 = 5 0 0 0 ( 1 + ( 0 . 0 6 K 3 ) )
A = 5900
C a m will h a v e $ 5 9 0 0 .
3. a) A = P ( 1 + rt)
P i s $1000; r i s 5 % o r 0 . 0 5 ; n s 5
.4 = 1 0 0 0 ( 1 + ( 0 , 0 5 ) ( 5 ) )
A = 1250
5.A
= P ( 1 + rt)
B r a d ' s G I C : P is $ 1 5 0 0 0 ; r i s 3 . 2 % o r 0 . 0 3 2 ' t is 6
/
I' Of 10(1 + ( 0 . 0 3 2 ) ( 6 ) )
' ' ' ' 7 mm
I he r.itu.e v a l u e o f B r a d ' s i n v e s t m e n t is $ 1 7 8 8 0
C i . r i - . G I C ; P is $ 1 5 0 0 0 ; r is 3 . 3 % o r 0 0 3 3 ' t is 5
^
15 0.30(1 + ( 0 , 0 3 3 ) ( 5 ) )
' 17 4 7 5
f f i C f u t u r e v a l u e o f C h r i s ' s i n v e s t m e n t is $ 1 7 4 7 5
B r a d ' s i n v e s t m e n t will h a v e a g r e a t e r f u t u r e v a l u e
at m a t u r i t y . I n v e s t i n g t h e m o n e y f o r o n e m o r e y e a r
r e s u l t s in m o r e i n t e r e s t e a r n e d t h a n d o e s i n v e s t i n q
t h e m o n e y at a 0,1 % h i g h e r i n t e r e s t r a t e .
T h e f u t u r e v a l u e is $ 1 2 5 0 .
Determine the interest e a r n e d .
1 2 5 0 ^ 1000 = 2 5 0
Rate of return =
^
1000
Rate of return = 0.25
T h e r a t e o f r e t u r n is 2 5 %
b | A 71 - P ( 1
-rrl)
P i s $ 1 0 5 0 ; r i s 5 % o r 0 . 0 5 ; f is 5
A = 1050(1 + (0.05)(5))
A = 1312.50
G.a}A
A
= P + Prt
$ 1 5 0 0 0 , F = $ 1 2 0 0 0 , f = 10
15 0 0 0 = 12 0 0 0 + ( l 2 0 0 0 ) ( r ) ( l 0 )
3 0 0 0 = 120 OOOr
^J3000_^
120 0 0 0
0.025 = f
A n i n t e r e s t r a t e o f 2 . 5 % is n e e d e d f o r t h e C S B to
g r o w t o $ 1 5 0 0 0 in 10 y e a r s .
T h e f u t u r e v a l u e is $ 1 3 1 2 . 5 0 .
F o u n d a t i o n s o f M a t h e m a t i c s 12 S o l u t i o n s M a n u a l
1-1
9 . a ) / t - ^'(1
li) A
l>
1
/ 'n
>h
$ 1 / i)U(l f
4
!)t;;,ir<^«' n
? ' . T . » 1 % ' y>3% or 0 . 0 3 5 . f
10
A
. $ •(>«}<). / V. ^
or 0 . 0 2 5 ; f is 0 , 5
'.h(iO( 1 1 (() i f ' 3 ) i ( i '41
A «>43
(ton, i t I " 0
i n v e s t m e n t is $ 3 6 4 5 .
A
10 3<}'i
! I,,, u i i u . r •^.i!u.- ',i 111.- t : S B w o u l d b e $ 1 6 2 0 0 .
l akiV-J C ' ^ ' i
7 . a l T h e y will b e e q u a l , e . g . , T h e p r i n c i p a l , i n t e r e s t r a t e ,
a n d t e r m a r e e q u a l . B o t h e a r n $ 3 0 0 in i n t e r e s t .
b | N o . e . g . . W i t h s i m p l e i n t e r e s t , t h e r e is n o a d v a n t a g e t o
h a v i n g it p a i d m o r e o f t e n .
m o n t h l y bill.
^ is 0.5
A ^ ''.^!.2 Of)
! h e hiiuiv
v a l u . « .4 I o l o y . f . n v e s t m e n t is $ 3 5 5 2 . 5 0 .
Of>|,;itfii,n(> I h o (lihr-ron'.f
:if,.13
c) e.g.. T h e y m a y need t h e interest m o n e y to pay a
' = •
53!)2 fT)
32 30
f j i " , i r r ( will h VJ'- i ' J . '
'<<>i«'5 t h a n L a t o y a a f t e r
6 months.
b) Desiree; 3645 - 3600 = 45
A , r 1-fM'UO ,
n
D e s i r e e will e a r n $ 4 5 in i n t e r e s t .
,'.%or0.05;fis5
I . i t o f a: 3552,50 - 3500 = 52.50
H, i . n i „ , • t ' ( l ' . , ( 5 ) )
L a t o y a will e a r n $ 5 2 . 5 0 in i n t e r e s t .
'jV„
a
- . . v e s t m e n t A is $ 1 2 5 0 0 ,
''r.'M.Juo.-
,
Determine the difference;
5 2 , 5 0 - 4 5 = 7.50
L a t o y a will e a r n $ 7 , 5 0 m o r e in i n t e r e s t t h a n D e s i r e e .
c) Desiree:
( . 4 % o r 0 , 0 1 4 ; f is 1 0
•)(10))
4
1.1.'.-'
fh
s>ui,
<4 : i v e s t m e n t B ! S $ 1 1 4 0 0 .
C
r a t e of r e t u r n
45
=
^
our. . .% 1.9% o r 0 . 0 1 9 ; f is 7
rate of return = 0.0125 or 1.25%
))(7))
e
Latofa:
' ^ A vO
tui.jrr
r) I ' ,
r.'
H.uf i n v e s t m e n t C i s $ 1 1 3 3 0 .
J . i h i.i«o . ='
5 .nof.C
rate of r e t u r n
0 5 % o r 0 . 0 1 0 5 ; f is 8
• . )0..05)(8))
rate of r e t u r n = 0 . 0 1 5 o r 1.5%
L a t o y a ' s r a t e of r e t u m is h i g h e r t h a n D e s i r e e ' s r a t e
l i n ; f u t u n - v ' ^ . u . _ of i r . v e s t m e n t D i s $ 1 0 8 4 0 ,
f i..<r 'JU .^f'•' r Ht l i o n t y v a l u e t o l e a s t : I n v e s t m e n t A ,
|,M..r^t H
b ) Mo
• i w e - s t m e n t C , I n v e s t m e n t D.
IS i n s i i l l . c k - n t t o c h a n g e r a n k i n g s .
| , , v - Jfii-f I i
l"JiO s e m i - a n n u a l l y , s o f = 5
,oO(.0^
~
1.5 o r 3 . 5 .
B . I n v e s t m e n t is p a i d a n n u a l l y . St. I
4
$ 1 0 0 0 0 ; r is 1.4%> o r 0.0 U ,
6 . 5 % or 0.065
10 0 0 0 + ( 1 0 0 0 0 ) ( 0 . 0 6 5 ) ( f )
5000=650f
It will t a k e S h a u n 8 y e a r s t o e a r n e n o u g h m o n e y t o
I h e t u i u i e <.aiue o l - w e s t m e n ^ A I • '1. i i 7 f - 0 ,
Pi'
. pff
f=7.69
031(3.5))
/on
A -
r
A is $ 1 3 0 0 0 ; P is $ 1 0 0 0 0 ; ris
15 0 0 0 -
f , S . 1 T " J 0 0 . .% 3 " / - o r 0 . 0 5 ; f is 3,5
4
of r e t u r n ,
10. A
M . the- . i i n o u n t of i n t e r e s t n o t e a r n e d in t h e last
1 s yci.ir
52.50
=
^
H.
2 or 8.
i 3
. ifiiMM)f1 + ( 0 . 0 1 4 ) ( 8 ) )
11. a ) 7 \ = P ( 1 + rt)
A is $ 2 0 0 0 0 ; r is 3 . 2 % o r 0 . 0 3 2 ; t is 5
20 000 = P(1 + (0.032)(5))
/ t - i l 120
T t i e f u t u r e v a l u e of i n v e s t m e n t B is $ 1 1 1 2 0 ,
I n v e s t m e n t is p a i d q u a r t e r l y , s o f is 7
make the down payment.
1.5 o r 5 , 5 ,
P i s $ 1 0 0 0 0 ; r i s i r / o o r 0 , 0 1 9 ; f is 5.5
20 000 = 1.16P
P = $17 241.38
b) 7\ = P + Prt
A is $ 2 5 0 0 0 ; P i- % 1 / 24 i
.3; r is 3 . 2 % o r 0 . 0 3 2
4 = 10 0 0 0 ( 1 + ( 0 , 0 1 9 ) ( 5 . 5 ) )
2 5 0 0 0 = 17 2 4 1 3 8 + ( 1 7 2 4 1 3 8 ) ( 0 . 0 3 2 ) ( f )
^ = 11 0 4 5
7758.62 = 551.72f
T h e f u t u r e v a l u e of i n v e s t m e n t C is $ 1 1 0 4 5 .
f = 14,06
D. I n v e s t m e n t is p a i d a n n u a l l y , s o f is 8 ^ 2 o r 6.
P ib $ 1 0 0 0 0 ; r is 1 . 0 5 % or 0 . 0 1 0 5 ; t is 6
A
- 10 000(1 + (0,0105)(6))
It will t a k e a b o u t 14.1 y e a r s f o r t h e G I C t o b e
$25 000.
A " 10 630
T h e i u t u r e v a l u e of i n v e s t m e n t D is $ 1 0 6 3 0 .
C h a p t e r 1: F i n a n c i a l M a t h e m a t i c s : i n v e s t i n g M o n e y
1-2
A is $9400; P is $4700; t is
L e s s o n 1.2: E x p l o r i n g C o m p o u n d
page 19
i
•
, •
interest
)
E v e : P is $3000: r is 4 % o r 0.04- t is 5
71 •-- Zmm^ + (0.04)(5))
A =
I n e a n n u a l i n t e r e s t rate is
I.-. >. + rt)
mm
• '• • '''-^ ' '(•-,<•-,. ( •-. .Oe • '.'.e">
I >l»ly f - • ,|,ir,jl (...,..
-i i , H
12,5%,
•'••''•'•=1'
''>"iiiU
T h e v a l u e o f t h e i n v e s t m e n t w o u l d b e $14 100.
1 3 . a ) T h e s l o p e o f tho g r a p h w o u l d i n c r e a s e if t h e
interest rate i n c r e a s e d . F o r e x a m p l e , t h e i n v e s t m e n t
c u r r e n t l y earr
n t e r e s t e v e r y 3 y e a r s , s o it h a s a
• 'ff-'V
, <
I t'nmApM
, 'AU'.-) . 0
slope of ^ . A steeper graph with a slope of |
b | e.g.. Similar: T h e y h a v e t h e s a m e intere-st r a t e T h e
situations a r e represented by a linear relation that slopes
u p w a r d t o t h e right. T h e g r a p h s relate m o n e y t o t i m e
The graphs have the same slope.
Different; They have different principals. T h e interest
g r a p h s t a r t s a t (0, 0) w h i l e t h e i n v e s t m e n t g r a p h s t a r t s a t
(0, 3 ) . T h e i n v e s t m e n t g r a p h s h o w s t h e v a l u e o f t h e
i n v e s t m e n t a n d t h e interest w h i l e t h e i n t e r e s t g r a p h o n l y
s h o w s o n l y t h e interest,
1 4 . T h e C S B G r a h a m b u y s in y e a r 1 is i n v e s t e d f o r
5 y e a r s . T h e C S B h e b u y s in y e a r 2 is i n v e s t e d f o r
4 y e a r s , a n d s o o n . T h e C S B h e b u y s in y e a r 5 wili b e
i n v e s t e d f o r 1 year. D e t e r m i n e t h e y e a r l y v a l u e o f t h e
SB then add the values together
I I
r. e > , . ; , .
Y'im_ ind
;
,
j
'
'
.1
,
V a l u e ($)
jfi/b
1 1 of
I 1.32
! 190
3370
f . M h a i i ' s ir.ve'4m*-nt will h e w o r t h 3 5 5 7 0 d f t c i 5 y e a r s
1 5 C a r o l e ' s a c c o u n t p a y s i n t e r e s t d a i l y s o s h e will e a r n
86 days of interest w h e n s h e withdraws h e r m o n e y
C o n v e r t 8 6 d a y s t o a f r a c t i o n o f a year86
= 0,235...
3D5
A = P{1 + rt)
P is $ 2 4 0 0 0 ; r is 5 , 2 % o r 0.052- t is 0 2 3 5
^ = 2 4 000(1 +(0.112X0,235,..))
^ = 24 294.049...
Carole withdrew $24 294.05 w h e n s h e closed her
savings account.
s . .,
.. • • ,
( I f " " j Yc-ar e i . e » i , 4 . i . .
11
VVP"..'
> '.i-l "O
;e, "
13374^59^
.•'"'JO
3 6 4 0 QR
Lciiiy s i r i v e s i m e n t is w o r t h $3649.96 a f t e r 5 y e a r s
C a l c u l a t e t h e d i f f e r e n c e in interest
3649.96 ^ 3600 = 49.96
L a r r y ' s i n v e s t m e n t e a r n e d $49.96 m o r e in i n t e r e s t
t h a n E v e ' s b e c a u s e his i n v e s t m e n t e a r n e d i n t e r e s t
o n t h e p r i n c i p a l a n d o n t h e a c c u m u l a t e d interest.
= P ( 1 + rt)
$6500; r is 5 . 1 % o r 0.051 - f is 4
)500(1 + (0.051 K 4 ) )
e a y n t A : P is
'826,00
n v e s t m e n t in a c c o u n t A is w o r t h $ 7 8 2 6 0 0
after four years,
OmTus^I
''^
"'^
°'
^ = P(1 + ( 0 . 0 4 8 K 1 ) )
C a l c u l a t e t h e interest 4 t i m e s , u s i n g t h e v a l u e o f 4
as the new value of P for each new year Use a
t a b l e t o o r q a n i z e t h e answerc;
YoiJi
_ »
_
_ _^
/_ „
Ic.fal
I
would
m e a n t h e i n v e s t m e n t is e a r n i n g $2 o f i n t e r e s t e v e r y
3 y e a r s . T h i s c o u l d o n l y h a p p e n if t h e i n t e r e s t rate
increased,
feer
., .
[ j _ _ _ T 3 ^
l4
'
]^
•
..
• '• "• -v ' i!'!. e> I' - . r , I
table to organize t h e answers.
A = 14100
• '
f,
,
A = P(i +(0.04)(1))
Pm $ 4 7 0 0 ; r i s 12,5% o r 0,125- f is 16
71 = 4700(1 +(0,125K16))
I
.,(t
, ,
_
'7 _
_
_
Principal f$|
t350fj ( l i i
0312
j / 1 3 3 9H
_ J nai
0012
00^
Os)
33
f4r,ih2.)]^
7fsi0.77
i h e i n v e s t n f c i i l in d o c o u n i b is w o r t h $ 7 8 4 0 7 7
after four years. Sydney should choose account B
b e c a u s e it will e a r n m o r e interest.
3. a ) e . g . , n o it is n o t p o s s i b l e t o tell a s t h e
p n n c i p a l s , interest rates, a n d t i m e l i n e s all differ
b H = P(1+rf)
I n v e s t m e n t A : initial P is $ 6 0 0 0 ; r is 1.2% o r
0 . 0 1 2 ; f is 1 (for 4 y e a r s ) .
4 - P ( 1 < (0.012)(1))
Principal ($1
600CL00
OOTZOC)^
6144J6
~
6218.60
0072.00
614486^
6293.23
Return o n investment A- 6 2 9 3 2 j
6000 = 293.23
F o y n d a t i o n s o f M a t h e m a t i c s 12 S o l u t i o n s M a n y a l
1-3
Investment
4
B^/'..;.,-.(HH.
n - e c u m
M S
i
5,l)fifl(1 i n j 0 4 M ' 4 i
By llu- till.; t'l
K.J,',i„"'n.nv.e,t,ur..t|> n/'.Cl ',f)lHI 14nu
l„vestmcmt (4-n.lMH r. $ muO. . ,s f.%-.r 0 ue. / r. !
(foi I. y<vir4
/,
/'(I . n) ubi{1))
I Year
P r i n c i p a l ($)
'
4(100 UO
I
0
1
I
•
; .f-in4 4 0
\ i
'
Ycar^endValijod) _
1440 no _
i if \"
i S44'«iO
!.'( uif.i (••->, ipv» ' . l i u i - i i l
'
/;•• sni-
.evf .ifin-nl
'Aiil d o u b l e in
10 n u VH.»-.
I •» 4('t.-nnin. > tht; .-ic teal 4 o u ! ) ! i i i o t : m e :
-fi,, p,it»to,.li - f f n u o ! h . - . i n ; » i o n n t e r e s t r a t e i s 6 . 8 % .
Iht; .,orrip()ui.4in.| p.-oud i;. oiu.n.i', o r o n c e p e r y e a r .
r i i f ' tenn (in v«v)f 4 ''• •"T.ntiwn
|ip-fuh!i.-volu*-!' d.,Ml4-3''fH.T. or $14 0 0 0 .
> A/U4
Of.
III.: f>n;iiK.!.i! aj»o!.e;sii-)n on m y c a l c u l a t o r :
Ihf. hn.ihliinj tin«; H' 3 4 yt: »% w h i c h IS v e r y
, S()44
01
f j , , . . . ; !o 14.
44n4 40
(in
i ' V t . ' l f4
1 n n | i } n"
ID '.4.".
-J. I) a}
_ _
! iv.Av\
. I ' d S ' i f - ' ) ! i<> -.U v'.virs.
^ j ')-^0? 4(1
' 4 4 / 4 ua
Hv 4..- 'U!
n,,/4U4
4UiiU
e,7''e.4
C
! -e 4 , r . tn< (|a, s5«%-l r e i n m e<' i i r / e ' . ' - i ' X ' i ' i
..1 . . , t h e i n v e s t m e n t will d o u b l e in
i. 1 V(>-»>-.
! , d.'i.'O! ..^'h J a c t u a l d o u b l i n g t i m e :
.
,r,.!.
S850. T h e a n n u a l i n t e r e s t r a t e is 9 . 2 % .
« . . s s c „ . 1.3: C o m p o u n d I n t e r e s t : F u t u r e V a l u e ,
f h e c o m p o u n d i n g p e n o d is m o n t h l y , o r 12 t i m e s
| - M t | e 5fl
per year.
The term (in years) is
unknown.
T h e f u t u r e v a l u e is d o u b l e $ 8 5 0 . o r $ 1 7 0 0 .
I used the financial application o n my calculator:
T h e d o u b l i n g t i m e is 7 5 6 y e a r s , w h i c h is v e r y
d o s e t o t h e e s t i m a t e of 7 , 8 3 y e a r s .
1(2)
Row:
cl
'''
''o15...
' 15,6
U s i n g t h e rule o f 7 2 , it t a k e s 4 . 6 2 y e a r s f o r t h e
1 = 0.341,
13.2
R o w 3: f =
I
_.,
i n v e s t m e n t t o d o u b l e in v a l u e .
= 3.3
3 5
—
3oO
I = 0.009,
Row 4: i =
3
(365)
' 12 I
I = P(1 + , f
T h e p n n e i p a l is 3 1 / 3 0 0 .
T h e a n n u a l i n t e r e s t r a t e is 1 5 . 6 % .
T h e c o m p o u n d i n g p e n o d is w e e k l y , o r 5 2 t i m e s p e r
year.
T h e term (in years) is
unknown.
T h e f u t u r e v a l u e is d o u b l e $ 1 2 5 0 0 , o r $ 2 5 0 0 0 .
1 used the financial application on my calculator;
T h e d o u b l i n g t i m e is 4 . 4 5 y e a r s , w h i c h is v e r y
P = 520; f = 4 . 5 % compounded monthly.
1= 2 : ^
close to t h e estimate of 4.62 years.
= 0.003 7 5 ; f = 8 y e a r s . n = 8 . 1 2 = 96
d) 1 1 = 2 6 . 6 6 6 . . .
A = 520(1 + 0 . 0 0 3 7 5 ) *
4 = 744.829...
T h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 7 4 4 . 8 3 .
744 829
- 520 = 224.829...
T h e t o t a l i n t e r e s t e a r n e d o n t h e i n v e s t m e n t is $ 2 2 4 . 8 3 .
b) P = 1400; r = 8.6% c o m p o u n d e d semi-annually,
j ^ M ¥ . = 0 0 4 3 ; f = 15 y e a r s , n = 15 • 2 = 3 0
2
^ = 1400(1 + 0 . 0 4 3 ) ^ °
A - 4 9 5 0 5 9 3 ..
T h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 4 9 5 0 . 5 9 .
4950 593
-^1400 = 3550.593...
T h e t o t a l i n t e r e s t e a r n e d o n t h e i n v e s t m e n t is $ 3 5 5 0 . 5 9 .
1.4
U s i n g t h e rule of 7 2 , it t a k e s 2 6 . 6 7 y e a r s for t h e
i n v e s t m e n t t o d o u b l e in v a l u e .
T h e p n n e i p a l is $ 4 0 0 0 0 .
T h e a n n u a l i n t e r e s t r a t e is 2 . 7 % .
T h e c o m p o u n d i n g p e r i o d is s e m i - a n n u a l , o r
2 times per year.
The term (in years) Is
unknown.
T h e f u t u r e v a l u e is d o u b l e $ 4 0 0 0 0 , o r $ 8 0 0 0 0 .
I used the finaneial application on my calculator:
T h e d o u b l i n g t i m e is 2 5 . 8 5 y e a r s , w h i c h is c l o s e t o
t h e e s t i m a t e of 2 6 . 6 7 y e a r s .
i i | a ) T h e p r i n c i p a l is $ 7 0 0 0 T h e a n n u a l i n t e r e s t r a t e is 6 J %
s
38, T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r
y e a r . T h e t e r m (in y e a r s ) is 3 5 ,
The future value
A = P(1 + /)"
A = 7000(1 +
A
is
unknown.
T h e c u r r e n t v a l u e of t h e i n v e s t m e n t w i t h i n t e r e s t
i.r!'|.
n,.irfihl-/ I , S I S Of,..- •! i
! ) ! ' . i!- , i '
!l.f. ri«(
Vf .11 .
QMm'f
1
Animal
Monthly
eotijijoiiriciisig
•.ooipf.ondmc}
n
B9 9 9 9 , 0 0 7 , , ,
{)
ca.n 4 < / '
,•() I 'M) • "
T h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 6 9 9 9 9 0 1 .
69 999.007... ^ 7000 = 62 999.007...
n v h 3M
^i3.'' 0 4
f.3
T h e t o t a l i n t e r e s t e a r n e d is $ 6 2 9 9 9 . 0 1 .
j f / ,
••4:i> 3 0
b ) T h e p n n e i p a l is $ 8 5 0 . T h e a n n u a l i n t e r e s t r a t e is 9 . 2 %
s o / = 0 0 9 2 . T h e e o m p o u n d i n g p e r i o d is m o n t h l y . T h e
\7o,-/
t e r m (in y e a r s ) is 2 0 ,
ll :3'
4s
jJ
^
I
'/
n/4,'. i f .
; ; n 4 i lT.
ih '•
1 0 3 / o» f
n = 2 0 • 12 = 2 4 0
The future
value
A = P(1 +
if
is
unknown
12 00C
A = 850(1 + 0,092f^'^
A = 5314.630...
I- i-f
T h e f u t u r e v a l u e o f t h e i n v e s t m e n t is $ 5 3 1 4 , 6 3 .
? < »s: .
• monthly
compounding
5314.630... - 8 5 0 = 4464.630...
T h e t o t a l i n t e r e s t e a r n e d is $ 4 4 6 4 6 3 .
• annual
c ) T h e p n n e i p a l is $ 1 2 5 0 0 .
' •')'.'i
T h e a n n u a l i n t e r e s t rate is 1 5 . 6 % s o i = 0 1 5 6 .
T h e c o m p o u n d i n g p e n o d is w e e k l y , o r 5 2 t i m e s p e r y e a r .
Xhrt t ^ r n -
< >••• > ]
c
" e a r s ) is 5.
0
le is
•
unknown.
c) A s c o m p o u n d i n g frequency increases, interest
rate g r o w t h i n c r e a s e s .
260
0.156)-
ih.(
1 h' : A-j-K .'.'i.je of t h e i n v e s t m e n t is $ 2 7 2 3 6 . 5 8 ,
2 / ' 4 3 3 3 - 1 t 5 0 0 = 14 7 3 6 . 5 8
I h c S 4 c 4 , n 4 . . iSt e a r n e d is $ 1 4 7 3 6 . 5 8 .
41 inr< p r ; i i , o ( . il is $ 4 0
U s i n g t h e rule o f 7 2 . it will t a k e 15 y e a r s for P a r k e r
t o d o u b l e his i n v e s t m e n t .
000.
i n e a n n u a l i n t e r e s t r a t e is 2 . 7 % s o i = 0 . 0 2 7
Using a financial application:
T h e c o m p o u n d i n g p e r i o d is s e m i - a n n u a l , o r 2 t i m e s p e r y e a r
T h e p n n e i p a l is $ 6 0 0 0 .
T h e t e r m (in y e a r s ) is 8.
T h e a n n u a l i n t e r e s t rate is 4 . 8 % .
n = 8 • 2 = 16
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r .
The future
value
A = P(1 4
if
is
unknown.
The term
(in years)
is
unknown.
T h e f u t u r e v a l u e is d o u b l e $ 6 0 0 0 . o r $ 1 2 0 0 0
46
A = 40 0 0 0 ( 1 + 0 . 0 2 7 ) '
T h e d o u b l i n g t i m e is 1 4 , 7 8 y e a r s , w h i c h is c l o s e t o
t h e e s t i m a t e of 15 y e a r s .
A = 49 5 7 2 . 4 1 0 . ..
T h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 4 9 5 7 2 . 4 1
49 572.41 - 40 000 = 9572.41
T h e t o t a l i n t e r e s t e a r n e d is $ 9 5 7 2 . 4 1 .
15 - 10 = 5
U s i n g t h e rule o f 7 2 , P a r k e r w o u l d b e a b l e t o b u y
4. a)
his m o t o r c y c l e 5 y e a r s s o o n e r .
P r i n c i p a l ($)
3000
Interest Rate per A n n u m
Periods per Year
^0.09
"ooot) ~
Using a financial application:
^ 0.09
T h e p n n e i p a l is $ 6 0 0 0 .
T h e a n n u a l i n t e r e s t r a t e is 7 . 2 % .
12
f
T h e c o m p o u n d i n g p e n o d is a n n u a l , o r o n c e p e r y e a r .
V a l u e at E n d o f Y e a r
o"
H
3000 ou""
3000 00
3885.09
3925 93
6
9
.3031.30
313/.66
6515.68
6723.37
12^
8437.99
8798 51
13
10 9 2 7 . 4 5
18
14 151.36 1
" ' 11 5 i 4 " r <
13 0 6 7 9 1 J
The term (in years)
is
unknown.
T h e f u t u r e v a l u e is d o u b l e $ 6 0 0 0 , o r $ 1 2 0 0 0 .
T h e d o u b l i n g t i m e is 9 . 9 7 y e a r s , w h i e h is c l o s e t o
t h e e s t i m a t e of 10 y e a r s .
14.78 - 9.97 = 4.81
P a r k e r w o u l d b e a b l e t o b u y his m o t o r c y c l e
4.81 years sooner.
T h e c u r r e n t v a l u e of t h e i n v e s t m e n t w i t h i n t e r e s t
c o m p o u n d e d a n n u a l l y is $ 1 4 1 5 1 . 3 6 .
F o u n d a t i o n s o f M a t h e m a t i c s 12 S o l u t i o n s M a n u a l
1-5
6. T h e p r i n c i p a l is $ 2 5 0 0 0 0 .
T h e a n n u a l interest r a t e is 3 . 8 % .
T h e c o m p o u n d i n g p e r i o d is s e m i - a n n u a l , o r 2 t i m e s p e r
y e a r . T h e t e r m (in y e a r s ) is 1.
r? = 1 • 2 = 2
The future value is
unknown.
/ I = P ( 1 + if
A - 2 3 0 onn(i I 0 033)-'
A - e s n nou oof!
1 IIP volur .)? Ih<- hu-st mod a f t e r o n e y e a r is $ 2 5 9 6 9 0 . 2 5 ,
' notjoo
. " , 0 f.9(i'OS
0590.25
ii„- Pu'.l tinid l'.:c. 39')',in 2 5 a v a i l a b l e e a c h y e a r .
Bool? A IS- o''.-- 'on! !S $20 000,
I ht .in.0.4 in>--i' '.I oti? I ; 6,6%.
1,,^
( f.p'.e
. 1 " . . ! i s
' n- i I.'''
y .>•
n = 2 •1 = 2
; I, '.j!'!!'•
-
•'I
i
a n n u a l , or o n c e per year.
''
<•/».'*•.'
wn.
/< i
I
/ e s t m e n t is $ 2 2 7 2 7 . 1 2
22 7
20 000 = 2727,12
2727.12
• = 0.136 356,.
20 000
Th
-.lO of r e t u r n o n t h e B a n k A i n v e s t m e n t is 13.64¥o.
S - i r * R: T h e p r i n c i p a l is $ 2 0 0 0 0 .
o;
luai i n t e r e s t rate is 6 , 5 5 % .
%i. . . o m p o u n d i n g p e r i o d is s e m i - a n n u a l , o r 2 t i m e s p e r y e a r .
T h e t e r m (in y e a r s ) is 2 .
n = 2 • 2 = 4
Ttie future
four times.
a)
X 4 = 48
' 6
U s i n g t h e rule o f 7 2 . it w i l l t a k e 4 8 y e a r s f o r $ 1 0 0 0
t o g r o w t o $ 1 6 0 0 0 at a n i n t e r e s t rate of 6 %
c o m p o u n d e d annually.
b) I ? x 4 = 24
' 12
U s i n g t h e rule o f 7 2 , it w i l l t a k e 2 4 y e a r s f o r $ 1 0 0 0
t o g r o w t o $ 1 6 0 0 0 at a n i n t e r e s t rate o f 1 2 %
c o m p o u n d e d annually.
9. T h e i n t e r e s t g r o w s by a bit m o r e t h a n $ 5 0 e a c h
year s o I will g u e s s that the pnneipal w a s $ 8 0 0 .
Use this value to d e t e r m i n e the interest rate.
T h e p n n e i p a l is $ 8 0 0 .
The annual interest rate is
unknown.
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r .
T h e t e r m (in y e a r s ) is 3.
5
/ O C)w{n
8. F o r $ 1 0 0 0 t o g r o w v 3 n . 0 0 0 . it w o u l d d o u b l e
value is
unknown.
A = P ( 1 + if
A = 20 0 0 0 ( 1 + 0 . 0 6 5 5 ) ^
A = 22 751,540...
T h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 2 2 7 5 1 . 5 4 .
The future value $966,36.
I used the financial application on my calculator;
t h e a n n u a l i n t e r e s t rate is 6 . 5 % .
T e s t t h e s e v a l u e s t o s e e if t h e y p r o d u c e t h e
c o r r e c t v a l u e of t h e i n v e s t m e n t in y e a r 2 .
T h e p n n e i p a l is $ 8 0 0 .
T h e a n n u a l i n t e r e s t rate is 6 . 5 % .
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r .
T h e t e r m (in y e a r s ) is 2.
The future value is
unknown.
I used the financial application on my calculator;
t h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 9 0 7 , 3 8 0 . .
If the p n n e i p a l is $ 8 0 0 a n d t h e a n n u a l i n t e r e s t rate
is 6 . 5 % . t h e v a l u e o f t h e i n v e s t m e n t a f t e r t w o y e a r s
IS $ 9 0 7 . 2 8 , w h i c h is t h e v a l u e g i v e n in t h e t a b l e .
T h e i n t e r e s t rate o f 6 . 5 % a n d p r i n c i p a l of $ 8 0 0 a r e
correct.
22 751.54 - 20 000 = 2751.54
10. F i r s t f o u r y e a r s : T h e p n n e i p a l is $ 4 0 0 0 0 .
R a t e of r e t u r n ;
= 0-137 5 7 7 . . .
T h e rate of r e t u r n o n t h e B a n k B i n v e s t m e n t is 1 3 . 7 6 % .
B a n k C : T h e p n n e i p a l is $ 2 0 0 0 0 .
T h e a n n u a l i n t e r e s t rate is 6 . 5 % .
T h e c o m p o u n d i n g p e r i o d is q u a r t e r l y , o r 4 t i m e s p e r y e a r .
T h e t e r m (in y e a r s ) is 2. n = 2 - 4 = 8
T h e future
value is
unknown.
A = P ( 1 + if
A = 20 000(1 + 0.065)"
A = 22 752.779...
T h e f u t u r e v a l u e o f t h e i n v e s t m e n t is $ 2 2 7 5 2 . 7 8 .
22 752.78 - 20 000 = 2752.78
R 3 , e of r e t u r n :
0.137 639..
T h e rate of r e t u r n o n t h e B a n k C i n v e s t m e n t is 1 3 . 7 6 % .
T h e rates from greatest to least return on investment are
6.5%. c o m p o u n d e d quarterly (13.76%, Bank C), 6.55%.
compounded semi-annually (13.75%, Bank B), and
6.6%. compounded annually (13.63%, Bank A).
1-6
T h e a n n u a l i n t e r e s t rate is 4 . 8 % .
T h e c o m p o u n d i n g p e n o d is s e m i - a n n u a l , o r t w i c e p e r y e a r .
T h e t e r m (in y e a r s ) is 4 . n = 4 • 2 = 8
lt,o future
value
is
unknown.
A--.PI1+0"
A ~ 40 000(1 + 0.048)"
A
4 0 357.032...
T h e v a l u e o f t h e i n v e s t m e n t a f t e r four y e a r s is
$48 357.03
L a s t t w o y e a r s : T h e p n n e i p a l is $ 4 8 3 5 7 . 0 3 .
T h e a n n u a l i n t e r e s t rate is 6 % .
T h e e o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r .
T h e t e r m (in y e a r s ) is 2 ,
0 = 2-1=2
The future value
A = P(1 +
is
unknown.
if
A = 4 8 3 5 7 . 0 3 2 . ..(1 + 0 . 0 6 ) '
A = 54 333.962. .
T h e t o t a l v a l u e o f t h e i n v e s t m e n t a f t e r six y e a r s is
$54 333.96,
C h a p t e r 1: F i n a n c i a l M a t h e m a t i c s : I n v e s t i n g M o n e y
F i r s t f o y r y e a r s : T h e p r i n c i p a l ^, ]. i ...e.
T h e a n n u a l i n t e r e s t r a t e is 9 % .
T h e c o m p o u n d i n g p e r i o d is semi-^annual, o r 2 t i m e s p e r y e a r
i i | e.g., T e n y e a r o p t i o n :
Advantage
__^isad¥antage
T h e t e r m (in y e a r s ) is 4 ,
G I C i n t e r e s t rate is
C a n n o t b e n e f i t if b a n k
0 = 4-2 = 8
s e c u r e if b a n k i n t e r e s t
interest rates
The future
value
4 = P(1 +
if
is
rise.
unknown,
D o n 4 need to think
Cannot reinvest the
A = 1500(1 + 0.09)^
about investment for ten
m o n e y for t e n y e a r s .
A = 2133,150...
years.
T h e v a l u e o f t h e i n v e s t m e n t a f t e r f o u r y e a r s is $ 2 1 3 3 . 1 5 .
L a s t two
y e a r s : T h e p r i n c i p a l is $ 2 1 3 3 , 1 5 .
T h e a n n u a l i n t e r e s t r a t e is 1 1 % ,
Five year twice o p t i o n :
Advatitage
Disadvantage
• -OM h( nefit f r o m h i g h e r
W i l l e a r n l e s s i n t e r e s t if
T h e c o m p o u n d i n g p e r i o d is m o n t h l y , o r 12 t i m e s p e r y e a r
T h e t e r m (in y e a r s ) is 2 .
,i
2-1
o/
The future
value
A = P{1 +
if
is
A = 2133,15(1 +
terest rates
bank interest rates drop
Jinvesting.
after five years.
nvest money.
unknown.
Interest rates need to
rise o v e r 3 . 2 5 % for total
investment to earn
OAlf*
s a m e interest as ten
/I = 2655,407,..
year option.
T h e t o t a l v a l u e o f t h e i n v e s t m e n t a f t e r six y e a r s is $ 2 6 5 5 . 4 1 .
eg.,
1 2 . a | e . g . . T h e h i g h e r i n t e r e s t r a t e is p a y m e n t in
exchange for more time before maturity.
b | i) 1 0 y e a r o p t i o n : T h e p n n e i p a l is $ 5 0 0 0 ,
f f4tnilar
j Different
Bofh investments pay
'~ \
! 4 o m p o u n d inten-s?
T h e a n n u a l i n t e r e s t r a t e is 3 . 2 5 % .
If.terest a s a p e r c e n t
' •. . - ' e s t m e n t s a l s o p a y
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r .
the pnneipal.
j i'sorest on previous
1
T h e t e r m (in y e a r s ) is 1 0 ,
The future value
71 = P ( 1 + if
terest earned.
b i h investments can
0 = 1 0 - 1 = 10
is
unknown.
npio interest
h , calculated using a
|
i^imula.
estments are easier
1
calculate b e c a u s e
ly h a v e f e w e r
A = 5000(1 + 0.0325)'°
A = 6884.471..,
iables
T h e v a l u e o f t h e i n v e s t m e n t a f t e r t e n y e a r s is $ 6 8 8 4 . 4 7 ,
F i v e y e a r t w i c e o p t i o n : T h e p r i n c i p a l is $ 5 0 0 0 .
T h e a n n u a l i n t e r e s t rate is 2 , 6 5 % .
Both investments
i n c r e a s e in v a l u e ovet
time.
' T j m p o u n d interest
e s t m e n t s i n c r e a s e in
vaiue more rapidly than
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r .
simple interest
T h e t e r m (in y e a r s ) is 5.
investments wilh the
0 =
5-1=5
The future
" -
A
" ' 1 -r
value
ne interest rate.
is
unknown.
if
1 4 . a ) T h e C S B P u d e e n b u y s in y e a r 1 is i n v e s t e d
'f»00(1 + 0 . 0 2 6 5 ) ^
for 5 y e a r s . T h e C S B s h e b u y s in y e a r 2 is
i n v e s t e d for 4 y e a r s , a n d s o o n . T h e C S B s h e b u y s
A ~ .)t-98.555...
, . J l u e o f t h e i n v e s t m e n t a f t e r f i v e y e a r s is $ 5 6 9 8 . 5 6
in y e a r 5 will be i n v e s t e d f o r 1 y e a r .
R e i n v e s t e d : T h e p r i n c i p a l is $ 5 6 9 8 . 5 6 .
Determine the yeady value of the five-year C S B
T h e a n n u a l i n t e r e s t r a t e is 2 . 6 5 % ,
then add the valuer toqether
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r
. P r i n c i p a l (J)
T h e t e r m (in y e a r s ) is 5,
f^A^l^jA
0 =
5-1=5
The future
A - P(1 +
A
value
if
] \
P e n o d s per Year
is
unknown.
"
f
„
~
J
J
„
^
^
I
lotnl
^
_^
^
~
I
^
^
^
^
y i i i f
529 64 "
545 IJ ~
561 03
^ ^
0
^
p
„
_
~
"lJJ.02tl^
_ [
1
5698.56(1 + 0.0265)^
" "^^^0
_
V a l u e at E rid of Year
A - 6494.706,.,
f h e v a l u e o f t h e i n v e s t m e n t a f t e r t e n y e a r s is $ 6 4 9 4 . 7 1 .
e.g., Interest rates are c o m p o u n d e d annually, interest
r a t e s r e m a i n t h e s a m e in 5 y e a r s , c a n r e i n v e s t all
$ 5 6 9 8 . 5 6 in 5 y e a r s .
^
f^ate p e r ^ A n j i n m
5 7 / 42 '
?Z^Z-8i^
T h e v a l u e of P u r i e e n ' s i n v e s t m e n t a f t e r f i v e y e a r s
is $ 2 7 2 7 8 1 .
I
F o u n d a t i o n s o f M a t h e m a t i c s 12 S o l u t i o n s M a n u a l
1-7
D
'><)()
'"Piinr.ipal ($)
j |i4cror.t
pft
Annum
Year
Savings (S)
20 1 I
5000 00
148 '
2012
2
I 14-ri(Kis |)f;r Y i ; a i
Mv i n v r s t i n m i t m o l u r o d allot 5 years: $5725.96
5 2 8 0 6()
i V n l u e at t i i 4 ..f Y e a r
1
ai
Ai I 1
!)42f) BSf
r.
594 24
4015
55//
/
f , l f 44
2 0 I <.
5>25 96
_
^
:
~8
y
'
\
2/2/
1 to ;>
'
'
ZZZZZZ
10
'
"
1441 4 1
E . I r o l ' o d ,i 1 M y i n v o s t i i i o n l ' s i n t e r e s t rate
447 94
d f n n;o%f:d l o 1 / 5 ' 4 . .
hbi] H'y
F
4 H / 7 4^.
k.r«!
; h . , v . i i u t ; n-i
$ 5 0 0 0 per yeat s i n c e my init.ai i n v e s t m e n t f o r a
total of $ 3 0 725.96.
(-nvinan;
• r n ; , r. 4 -/(-..iis
• c-;cin<<i.
4, . m n n
hifjlu.-i m i e n ' O f fnf(;
i i r ' n v f . . t f ' d m y ^.ovirvj'- $ 4 / 2 - ' i 4 6 , a n d i n v e s t e d
irr./f-.'r.sf-if a f t n i t:;n y e a r ;
».f of j «; . c -
:,',< 4 . i v w i | . / 5 - . n
-ijfi. f.,j
I i n v . v d f d III t n e 5 yf.'or ' - . I ' . <.nce m o r e , s i n c e it
l i , o . inn
$5877.96.
I'J
19
t...\ii
f.ui
! f"- 4 i . f H ; .i<
- 1- .', fifitif.if
G . I r e a c h e d m y g o a l o f 1 m i l l i o n in 2 1 2 8 , w h e n I
4-'• i. >st 4f p: • <? (4
I ' • 1 .' iti«
,<MV nt
i=c . . i , . , y.Mn> . . ^ u i '
'f:
H. I n o t i c e d t h a t w h e n i n v e s t i n g in a 5 - y e a r G I C , I
would not invest more m o n e y for another 5 years.
)!-•/»•!•./ '"AO 7 n n r ,
i r - i . ; •! K uf 4i.-
would be 139.
! > - V C J I .Kjpussl . it
'
'7
W h e n I c o m p a r e d t h e r e s u l t s o f a 1-year G I C o v e r
10 y e a r s a n d a 5 - y e a r G I C o v e r 10 y e a r s , I n o t i c e d
, i ' i 4 4i^; d« t . ' r n l - 4 I ' H J i ' . O d
that t h e 5-year G I C performed better than the
, i'.HH ip ii f 4 ; _
1-year G I C o n l y in t h e 1 0 t h y e a r . T h e r e f o r e , a
s t r a t e g y t h a t w o u l d r e s u l t in t h e l e a s t a g e t o r e a c h
r c n » ! 4 s pof 7fM<
m y g o a l w o u l d h a v e m e i n v e s t $ 5 0 0 0 p e r y e a r in a
I V'5lu( . i l l m l <•> fe.Jf
1-year G I C f o r t h e first 5 - 9 y e a r s t o i n c r e a s e m y
4<ji
^ "
:
1}
tiC
L Z Z Z Z I ^ ^
i
4
I
,
r
The w
^ 5 2 2 5-'
4 ? f.4
h . f a i Will-
principal as fast as possible. T h e n , I would invest
i i ' ^ p o r i t ".1
in a s e r i e s o f 5 - y e a r G I C s until I r e a c h e d m y g o a l ,
noi' Of4 on
VIJ4V ni]
since t h e 5-year G I C yields a higher interest rate.
i422 42
^ 5168
14»
of 4 nv"^- - n - f - o i t n t - n t a
$5168.65.
I. T h e o u t c o m e o f t h e d i e roll a f f e c t e d m y
investment m u c h more than the strategy I w a s
using, since m y interest rate w o u l d s o m e t i m e s dip
b e l o w 0, m e a n i n g m y i n v e s t m e n t lost v a l u e .
J . Since savings accounts, GICs, and Canada
Savings B o n d s d o not have negative interest rates,
it w o u l d m a k e s e n s e n o t t o let t h e r a t e s g o b e l o w
z e r o . M o r e o v e r , t h e B a n k o f C a n a d a a d j u s t s its
History C o n n e c t i o n , p a g e 32
A . r . p . a t t h e s t a r t o f t h e 1 9 5 0 s , t h e i n t e r e s t rate w a s
2 5 % . T h e i n t e r e s t rate i n c r e a s e d s l o w l y o v e r t h e first
half o f t h e d e c a d e a n d , b y t h e e n d o f t h e d e c a d e , it w a s
i n t e r e s t r a t e b a s e d o n i n f l a t i o n , t o k e e p inflation
between 1 % and 2 % . Depending on the
i n v e s t m e n t , it w o u l d b e r e a s o n a b l e n o t t o let r a t e s
for the C a n a d a Savings Bond go below 0 . 5 % or
5%.
e x c e e d 5 % . A n y d i e roll t h a t w o u l d r e s u l t in t h e
B. T h e best time to invest w o u l d h a v e b e e n at the e n d of
C S B r a t e g o i n g o u t s i d e t h e s e limits c o u l d b e
t h e 1 9 5 0 s , w h e n t h e i n t e r e s t rates w e r e a t t h e i r h i g h e s t
considered as "no changeT
for t h e d e c a d e .
T h e s e modifications could m e a n that I could reach
my investment goal faster, since I would never lose
Applying Problem-Solving Strategies, page 33
m o n e y in a n y p e r i o d . O n t h e o t h e r h a n d , it c o u l d
A
a l s o r e s u l t in r e a c h i n g m y i n v e s t m e n t g o a l m o r e
I will start s a v i n g in 2 0 1 6 .
s l o w l y , s i n c e t h e i n t e r e s t rate o n t h e C S B c o u l d
B. Research results
never exceed 5%.
Savings accouru
,
1 bO%_
GIC (1-year)
'
1 45%
GIC (Ssyearl
2 /5%_
Canada Savings Bond
0.65%
K. M y m o d i f i e d r u l e s a c t u a l l y d e c r e a s e d t h e a g e a t
which I reached the goal. Following the investment
s t r a t e g y o f a 1-year G I C f o r t h e first 10 y e a r s , t h e n
a 5 - y e a r G I C t h e r e a f t e r , I r e a c h e d m y g o a l in 2 0 7 6 .
when I would be 87.
All t h e s e i n v e s t m e n t s c o m p o u n d d a i l y .
C . I c h o s e t o i n v e s t m y $ 5 0 0 0 in t h e 5 - y e a r G I C .
1-8
Chapter 1 Financial Mathematics: Investing Money
T o r e a c h m y g o a l at a m o r e r e a s o n a b l e a g e t h e r u l e s
c o u l d b e c h a n g e d to a l l o w a l a r g e r i n v e s t m e n t e a c h y e a r
O r . t h e r u l e s c o u l d b e c h a n g e d t o a l l o w a n i n v e s t m e n t of
$ 5 0 0 0 in o n e 5 - y e a r G I C e a c h y e a r , i n s t e a d of e v e r y
5 years.
7!'.r/ 2 . •. . e r m i n e t h e a n n u a l i n t e r e s t r a t e
• v a l u e is $ 2 0 0 0 .
•nterest
'
••
rate is
unknown.
e n d i n g p e n o d is s e m i - a n n u a l , o r
/ear.
0 f I. >..- (.., y e a r s ) is 5
Lessoo i 4
page 40
•
^^npounci Interest: P r e s e n t
¥alye
alue is $ 3 5 0 0 .
' ' m.; .
, 4 c u l a t o r , t h e a n n u a l i n t e r e s t r a t e is 1 1 . 5 % .
11'.,%'} 3. I ) . i . j r m i n e t h e p r e s e n t v a l u e .
1 . I n v e s t m e n t B will r e q u i r e a g r e a t e r p r e s e n t v a l u e t o be
i n v e s t e d b e e a u s e t h e c o m p o u n d i n g f r e q u e n c y in l e s s
than for investment A,
P =
^ ^ ^
(To/)"
^ = 0 . 0 0 6 . 0 = 48
v a l u e is $ 8 2 5 4 . 4 8 .
I n v e s t m e n t A : A = 10 0 0 0 , i = ^
,
12
o = 120
Ut.vj
4
I )• i--rmine t h e i n v e s t m e n t t e r m ,
v a l u e is 6 0 9 . 3 5 .
i t e r e s t r a t e is 1 3 . 6 % .
10 0 0 0
l d i n g p e r i o d is a n n u a l , o r o n c e p e r
1+
0.05
12
P
years)
6071 61
T h e p r e s e n t v a l u e o f i n v e s t m e n t A is $ 6 0 7 1 . 6 1 .
I n v e s t m e n t B : A = 10 0 0 0 , / = 0 . 0 1 2 5 . n = 4 0
is
unknown.
Iue is $ 1 0 0 0 0 0 . 0 0 .
<
'rK,
' '
.;culator, t h e t e r m o f t h e i n v e s t m e n t is
40 y e a r s .
f't'^-vi 5 o"- - o m i n e t h e a n n u a l i n t e r e s t r a t e
T h e p r e s e n t v a l u e is $ 1 6 1 5 0 . 0 0 .
P
(1 + 0 . 0 1 2 5 ) *
The annual
6084.13
T h e c o m p o u n d i n g p e r i o d is m o n t h l y , o r 12 t i m e s p e r
T h e p r e s e n t v a l u e o f i n v e s t m e n t B is $ 6 0 8 4 . 1 3
Investment B requires a higher present value.
interest
rate is
unlinown.
year.
T h e t e r m (in y e a r s ) is 2.
T h e f u t u r e v a l u e is $ 2 3 5 0 0 . 0 0 .
S' i o v t - s f . j t e n t A :
/-•
-O ,1,'.'
P
6071.61
M
^ = 1647_,,
/'
I n v e s t m e n t B:
U s i n g m y c a l c u l a t o r , t h e a n n u a l i n t e r e s t r a t e is 1 8 . 9 % .
4 . a) P
A = 260 000, I = 0.085. o = 20
p^_250J)00_
(1+ 0.085)"°
A _ 10 0 0 0
P
" 6084.13
643..
T h e f u t u r e v a l u e t o p r e s e n t v a l u e ratio for I n v e s t m e n t A
IS 1 . 6 4 7 . . . a n d f o r i n v e s t m e n t B is 1 . 6 4 3 . . .
b) T h e investment with annually c o m p o u n d e d interest
w o u l d h a v e a h i g h e r ratio b e c a u s e t h e i n t e r e s t r a t e is
h i g h e r a n d t h e p r i n c i p a l is l o w e r . W i t h a 6 % i n t e r e s t rate
c o m p o u n d e d annually and a future value of $10 000 the
present value must be $5583.95. Since the principal'is
l o w e r t h a n b o t h i n v e s t m e n t A a n d B, t h e ratio will be
higher.
P
48 904.097. „
M a c should invest $48 9 0 4 . 1 0 n o w to h a v e
$ 2 5 0 0 0 0 in 2 0 y e a r s .
b) 250 000 ^ 48 904.10 = 201 095,90
T h e i n v e s t m e n t wiil e a r n $ 2 0 1 0 9 5 . 9 0 in i n t e r e s t in
20 years
5. a ) T h e p r e s e n t v a l u e is $ 9 0 0 0 .
The annual
interest
rate is
unknown.
T h e c o m p o u n d i n g p e r i o d is q u a r t e r i y , o r 4 t i m e s
per year.
T h e t e r m (in y e a r s ) is 2 ,
T h e f u t u r e v a l u e is $ 1 7 0 0 0 ,
3. R o w 1 : D e t e r m i n e t h e p r e s e n t v a l u e
P =
^
(1 + / ) "
J o s e p p i e w o u l d n e e d a n a n n u a l interest rate of
3 3 . 1 % t o m e e t his g o a l . T h i s is not r e a s o n a b l e .
Current interest rates for savings a c c o u n t s are
0 , 5 % t o 1.25%.
A = 2500, / = 0.078, n = 8
T h e p r e s e n t v a l u e is $ 1 3 7 0 . 8 5 .
F o y n d a t i o n s o f M a t h e m a t i c s 12 S o l y t i o n s M a n u a l
1-9
b ) T h e p r e s e n t v a l u e is $ 9 0 0 0 ,
T h e a n n u a l i n t e r e s t rate is 1 2 % .
Option
T h e c o m p o u n d i n g p e r i o d is q u a r t e r l y , or 4 t i m e s per y e a r .
The term
(in years)
is
A
3<384
(} .124 3 3 3
4 3 1 13 2 2
unknown.
T h e f u t u r e v a l u e is $ 1 7 0 0 0 .
3 8 9 1 43
U s i n g m y c a l c u l a t o r , it will t a k e J o s e p p i e 5.4 y e a r s t o h a v e
0 .',2^. ; r 7 )
18^108 57
$17 000.
386/,63
f)..;2:!. (4)1
18 132 3 5
A
6. P
Rate of R e t u r n
C l a i r e h a s t o i n v e s t $ 1 0 0 7 3 . 3 9 now t o h a v e $ 1 7 5 0 0 in t e n
Opti.;r, B h a s IIlO y r f i o t e s i o 4 e of r r d o n i at 32 3 3 ' 4
Sasha should choose option B so that she earns
the most interest on her investment,
b) S a s h a w o u l d earn $ 5 8 9 1 . 4 3 on her investment
years.
b y c h o o s i n g o p t i o n B.
(iZTf
A = 17 5 0 t : /
o -.'28, o = 2 0
>hf i>.ir:fi'i
s/,m(f i .
T h e a n n u a l inti . -,1 f.J,.- s 4 • ' } %
|„>ii, 4 <% ototiK.
• ill I iMj,>'»
,11 - o >f> >.r
in.
mknowr}.
once per year.
:
A
(1 + f T
24 0 0 0
(l + 0.0480f
P
1 n-y. ii
41
<3 4 0 !
P r m o i p a l {%)
10 o<-<; ; 35 o n e
4 01*'
o 070
interest Rate ppr
u '.7:H
Aiimim _ _ ^ _
;_
P e r i o d s p e r ~feat^ I '
V a l y e at^EncJ o f Y e a r
^ 1 4 101 C4> I • / 3 6 6 6 4
13 3 7 o 4 /
^
^ 17 4 4 3 2 ^ "
4 0 106 03_ _i 10 l / 2 ' » j i
0 = 6-1=6
p =
8 O p t i o n A : e . g . . I n c r e a s e t h e i n t e r e s t rate t o
T fi% in p a r t h) a n d d e c r e a s e t h e i n t e r e s t rate t o
18 1 1 5 . 2 1 7 . . ,
T h e p r e s e n t v a l u e of o p t i o n A is $ 1 8 1 1 5 , 2 2 .
Interest e a r n e d : 24 000
18 1 1 5 , 2 2 - 5 8 8 4 , 7 8
O p t i o n B : T f i e present value is
unknown.
T h e a n n u a l i n t e r e s t rate is 4 . 7 5 ° 4 .
_6_
~\'6'ik'1i'T
2 0 2 1 4 «3<
41 7 8 0 i 3
232/907
' .-'fl 0^)1 9 0
^ ' 2i;4 2 /
_ 1 0 i T T + \
• / 4 i l 52
' 18 1 0 6 . 4 4
Ol. Mil
T h e c o m p o u n d i n g p e r i o d is s e m i - a n n u a l , o r 2 t i m e s p e r y e a r .
T h e t e r m (in y e a r s ) is 6 y e a r s .
/ ' CO' 5
T h e f u t u r e v a l u e is $ 2 4 0 0 0 ,
v. ri(.13
1 J'H !
ISOuC
1-CM.n
! i , r. M - i / o r
P_ p : 443 3 / 1 ,.
4 h o I o / . e r u v . i l u e o f opti<'i« % o 4 4 3 108.57.
I n i e i p s t f n m e d 2 4 0 0 0 ^ 18 103 3 / ^ 5 8 9 1 . 4 3
O p t i o n C : The present value is unknown.
T h e a n n u a l i n t e r e s t rate is 4 . 7 0 % ,
T h e c o m p o u n d i n g p e r i o d is q u a r t e r t y , o r 4 t i m e s per y e a r .
T h e t e r m (in y e a r s ) is 6 y e a r s .
T h e f u t u r e v a l u e is $ 2 4 0 0 0 ,
24
.(> SCO
i'OMiC
t r o O . r
Ye.its
Valye ot iri¥_estmenti$|
(years!
0
A
^
(111)'
P
24
^ 8
0 0 0 _
10
15 0 0 0
15 0 0 0
3=)
T3JJ00
„
J6101:^»t)^!-'^Z i 0 4 ) M ^
V 4 T 1 2 8 • 30 100 6 8 ^
1 8 761454 I " 2 ^ 2 79 0:3
[o
"^fML.
10 172.90
2 0 2T4^83 , 2 6 OOJ .9<T
21 780 3 3 ^ 3 1 204.27
1/4^7.52
16 7 9 3 . 3 1
18 106.44
MiS)0470r
P
18 1 3 2 , 3 5 1 . . ,
ifdetesiecimed: 24 0 0 0 -
i
L35 = 5867.65
Chapter 1: Financial M a t h e m a t i c s : Investing M o n e f
1-10
GIC Investment Value
per Year
d ) T h e g r a p h s start at the s a m e point. Increasing the
i n t e r e s t rate m a d e t h e g r a p h s t e e p e r a n d it i n c r e a s e d
f a s t e r . D e c r e a s i n g t h e i n t e r e s t rate m a d e t h e g r a p h l e s s
s t e e p a n d it i n c r e a s e d m o r e s l o w l y .
O p t i o n B : e . g . , D e c r e a s e t h e p n n c i p a i t o $ 2 0 0 0 0 in p a r t
b) a n d i n c r e a s e t h e p n n c i p a i t o $ 3 0 0 0 0 in p a r t c ) .
1 b!
a|
• i
t
(...f l $ |
terest
terest
^ f i i S ' r i e< K o t o p.cr
' P e n . ••3-v p»'t Vr-,(t
terest
I
' y c ' i o . ; o l f u d Of Yr-or "
I
3
I3T226765
4
1 3 3 192.74
4^
s*
"1
'S
/
259.2:
'.30/ / ,
'j.-O 3f
3 - 0'
i 10 -0
'
; ; ."CO. Co
^o c .'. f •
o."
I /': i / 0 , I ^
\:IOOm C;0
OOi.iiS I i j .
;i5-4-o n y
31 C
lart c )
1000.00
3325.66
1664,57
29 C
9017.28
27 C
1384.34
4? 25 C
d ) T h e g r a p h s s t a r t a t t h e s a m e point. D e c r e a s i n g t h e
interest rate m a d e the graphs less steep and they
i n c r e a s e d m o r e s l o w l y . T h e d i s t a n c e b e t w e e n p o i n t s in
the s a m e year beoame larger as time increased.
srest
J
m 23 C
>
GIC
p. i r f o r •
:->Ol>0 0 0
21 C
19C
9. O p t i o n C will a l l o w B l a k e t o i n v e s t t h e l e a s t a n d
still m e e t his g o a l . It h a d t h e h i g h e s t a n n u a l
i n t e r e s t rate a n d t h e s e c o n d m o s t f r e g u e n t
compounding period.
17C
15 Of
O p t i o n A : The present value is
unknown.
T h e a n n u a l i n t e r e s t rate is 1 2 . 6 % .
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r
year.
T h e t e r m (in y e a r s ) is 4 0 y e a r s .
T h e f u t u r e v a l u e is 1 0 0 0 0 0 0 ,
Years
Time
(years)
Vail
• sm:O0!j4_,'
p.'-it ho
pari
26 000
' / O OfH)
1
2 7 t. M'. 'to ^
2
29 3 / / 94
3
4
31 2 2 0 6 3
3
35 23'. 03
3319' / -
I
30 ^)no
31 3,33 H
/ 5 3 ' ?2
3 9 7 4 2 i 3 T 4<.»6
\}A 02U
jti 030
2 ' 2 5 3 2 35_
3 8 23^9
^ / 4 W 43
4 0 / 41
n = 40 . 1 = 40
'4,
4^,
28^
(1+0"
f,4
I n o n fjijO
d ) e . g . . C h a n g i n g t h e p r i n c i p a l d o e s not c h a n g e t h e s l o p e of
the graph. Increasing the principal m o v e d the graph up and
decreasing the principal m o v e d the graph d o w n .
O p t i o n C : e . g . . D e c r e a s e t h e i n t e r e s t rate t o 3 % in part
b) a n d d e c r e a s e t h e i n t e r e s t rate t o 2 % in part c ) .
3)
b)
P r i n c i p a l ($)
8000
8000
'c)
8000
Interest Rate per
Annum
0.041
0T03
1 0 002
Periods per Year
4
4
4
'
'.10
r
lyo)
06/H 393..
1 hc p i e s e n t v a l u e of o p t i o n A is $ 8 6 7 8 . 8 9 .
O p t i o n B : The present value is
unknown.
T h e a n n u a l i n t e r e s t rate is 1 1 . 9 % .
T h e c o m p o u n d i n g p e n o d is s e m i - a n n u a l , o r
2 times per year.
T h e t e r m (in y e a r s ) is 4 0 y e a r s .
T h e f u t u r e v a l u e is 1 0 0 0 0 0 0 .
o = 40 2 = 80
Value at E n d of Year
2
^868(5
8492 / 9
8325 66
4
" 9417.85
9 0 15 94
8664 57
^ 6
10 2 1 8 3 9
9 5 7 1 41
" 8
1 1 086 99
10 1 6 0 . 8 9
9017 28
\ 9384
F o u n d a t i o n s o f M a t h e m a t i c s 12 S o l u t i o n s M a n u a l
111
OHIO
A ^
UH H)
1 ono 000
.t'iO
I
I
n ! 0 !IOI
r
C O , lh«> i.ilK. -Aouid d e c r e a s e if t h e i n t e r e s t w e r e
OHI:',
c o m p ( « ; n d . - d .iniia<4ly, A t o w e r e o m p o u n d i n g
I I H ; pt<-:.fjil v a l u t ; o l o p t i o n B IS $ 9 8 1 5 , 7 4 ,
fre q u o i n , y - A o o l d . e d u c e t h e f u t u r e v a l u e b u t n o t
O p t i o o C : I In - pii-r:{int
c h a n g e She p n - r . c m v a l u e , m a k i n g t h e ratio s m a l l e r .
value
is
unknown.
111.. o n i i i i , i l i i i l o n ;,l t a t e is 1 3 . 2 % .
T h t ; pio-scnl v a l u t ; is $ 3 0 0 0 .
1 h r <,()nipf)un4inq p j j r i o d is q u a r t e r l y , o r 4 t i m e s p e r y e a r .
The* o n n u . i l >Mterf.si r a t e is 8 . 5 6 % .
! Ill - if-nt! (iii y ! - . n - , j is 4 0 y e a r s .
T h e f-.dmpfJoodiiK) o e r i o d is a n n u a l , o r o n c e p e r y e a r .
Int.- l u l l . ! / ; v ; i ! o s ; I , ! 0 0 0
T h e f e : i n («n y e . H . o is 10 y e a r s .
n = 40-4=
000,
160
n = 10 - 1 = 10
F4f," thfiift
(1+iT
I OOP 0 0 0
•
J iKie is
''(It
A
>oo(4 I ^ ' ) . 0 8 5 6 ) ^ °
'» - f.32(S '•-'>
lh'
M- 1 3 2 f °
unknown
A
.
f i j k ' i e v . 4 , e of t h e i n v e s t m e n t w i t h i n t e r e s t
eoi:,f.,,.u :4f o . m n u a l l y is $ 6 8 2 0 5 5 .
P = 5545.600..,
",
T h e p r e s e n t v a l u e of o p t i o n C is $ 5 5 4 5 . 6 0 .
O p t i o n D : The present
value
is
unknown.
O.'O-'I'OS
I'
3000
T h e a n n u a l i n t e r e s t r a t e is 1 1 . 5 3 % .
273..
T h e c o m p o u n d i n g p e r i o d is w e e k l y , or 5 2 t i m e s p e r y e a r .
The
r-r, Un y e a r s ) is 4 0 y e a r s .
It.' IvK. d e c i m a l p l a c e s , t h e ratio w o u l d d e c r e a s e t o
T h e t o t u r e > a l u e is 1 0 0 0 0 0 0 .
n = 4o
--
2080
1 2 . The present
value
Is
unknown.
T h e a n n u a l i n t e r e s t r a t e is 5 . 3 % .
T h e c o m p o u n d i n g p e r i o d is m o n t h l y , or 12 t i m e s
per year.
3 000
M i l l
T h e t e r m (in y e a r s ) is 0 7 5 y e a r s .
T h e f u t u r e v a l u e is $ 4 7 6 5 . 3 0 .
1153)"
0 = 0 . 7 5 - 12 = 9
P = 9982.772,,,
T h e p r e s e n t v a l u e o f o p t i o n D is $ 9 9 8 2 . 7 7 .
A
O p t i o n C h a s t h e l o w e s t p r e s e n t v a l u e , s o it is t h e b e s t
(Uif
option for Blake.
.30
1 0 . F r a n c o m a d e t h e g r e a t e r original i n v e s t m e n t
• 1 + 0 053)
b e c a u s e investments with a n n u a l c o m p o u n d interest
r
earn less than i n v e s t m e n t s with monthly c o m p o u n d e d
T h e prf;<^eiit v a l u e o f D a n i e l ' s i n v e s t m e n t is
interest (and the s a m e a n n u a l interest rate).
r j r i j H yy
David
Future Value (S;
2 5 oorr
_ 25 000
Interest Rah
0 04'<
i 0 06O
oer
4 3 / 9 995,,,
$ 4 5 7 9 . 9 9 5 . .. o r $ 4 5 8 0 .
4765.30 - 4 5 7 9 . 9 9 5 . . . = 185,304...
T h e a c c o u n t h a s e a r n e d $ 1 8 5 . 3 0 in i n t e r e s t .
Annum
1 3 . The present
P e n o d s per Y e a r
T h e a n n u a l i n t e r e s t r a t e is 5 . 5 % .
Present Value ($)
3377.60-31/4] 40
I
.40
N u m b e r of Y e a r s
i TT'~7 60
204
7011
1^5 4 7 ' M O
1 1 . a ) T h e p r e s e n t v a l u e is $ 3 0 0 0 .
annual
interest
rate is
unknown.
T h e c o m p o u n d i n g p e r i o d is s e m i - a n n u a l , o r
2 times per year.
T h e f u t u r e v a l u e is $ 1 5 0 0 0 ,
n - 10
unknown.
i l j f
T h e t e r m (in y e a r s ) is 1 0 .
T h e f u t u r e v a l u e is $ 7 0 0 0 .
2 ^ 20
A
T h e c o m p o u n d i n g p e r i o d is q u a r t e r l y , o r 4 t i m e s p e r y e a r .
P
15 0 0 0
I used the financial application o n my calculator: Lucy
{1 I 0 0 5 5 ]
n e e d s a n a n n u a l i n t e r e s t r a t e of 8 . 5 6 % to m e e t h e r g o a l .
8 / 1 8 76,.,
1-12
is
T h e t e r m (in y e a r s ) is 10 y e a r s .
2fl
Franco invested $204.20 more than David.
The
value
Chapter 1: Financial Mathematics: Investing Money
' f - 'I
j;"4"'
'•'
• >'• h -.ifj;!..,,
0.
|r„v.-: . n l . - K - . M , J l e V./.I4 „ . , . „
<".Hj,r,„.,di,,., - / o i . c . n . n r .
f
• " * • ••fop'Hind ;o' -,...,{ , . . „ j . . , , „ fh,
' ' • • / • - • " 'In a! .1 3. ,hi I ii;|..N •.» i , i p . wi!r.
Ol"-U' ' ,.; p...l,,0,r,.j I j , . , . , , , „ ^ , ,, j ^,1^,
: .• ,t , . . , . 1
' •' '
• m,.
"
T . - . l i . Uf,-
M i c l - t 3 l i o p t e « fipvhim.
^l>.-.H,...,:l,.i,,,.,.,,..,;.,,,j
'.
/
pacje 4 5
/
^' ' $
'
/ I . 3 1 .n ,
0 ,ti
''
'•"
30 t ..r><4/|} oo(».|-;,/,
..-O Oil • : U Hi!
lO.O'
.•:-,<,I.!.i i: il,,..
r-< . { I ^
A
i rj,-:
- ':.»,!{„„,,. ,
•'^"•'"'•l'^-.'y'';',.fl,.;M.,.fti-^. e-f-Mf.
' V I -/'III
'
'•
'
'
3
(M.s.tif
,)
1 V - ir'
•
".T''!;'
o - 3of:4-j ,
r
o
f / 0- - i . H
$ 1 0 0 SO m y f u t u r e v a l u e
T h e p r e s e n t v a l u e is $ 1 0 0 .
' ' " - O ' " - ' Imo pc o - . ' ,
c,-,- rteriy, o r 4 t i m e s per year
' ' ' f
'
• " • • ' T ' *:..• I'llf O' 4 .viii bl.' ,,.-i,4 oo< <i4
'O
o
,if,.p
T h e f u t u r e v a l u e is $ 3 0 0 .
- I
,n m y c a l c u l a t o r ; A n
' m - u , - . . r - i . ' • „ 0 y o . ,v..-i -,:f<„v the investment t o triple
n-'Oiy 1 ' y.-j,-.,
•^^i a j : h ) p o " 1,1-; j.ilm
.< -nli.pO.
f h o . m r i o o l m h r-'-sf l o f e r.
Ihv c o o i p f o o O i o o p . T M O , o o t i o a l , o r o n c e p e r y e a r
T h e Lone ur.
4
i
< Of KorOfr^ifsr
•= *'33 5 "
T
0341 32
times
rate is
unknown.
v a l u e is $ 1 0 0 0 .
interest
rate is
15~
unknown.
T h e compounding p e r i o d is monthly, o r 12
T h e t e r m (in y e a r s ) is 1 y e a r ,
T h e f u t u r e v a l u e is $ 1 0 5 0 .
T h e a n n u a l interest r a t e is 4 . 8 9 % .
Year"
5
T h e a n n u a l interest rate is 4 , 9 1 %
present
J ? 335
79
B r a d P r. I h o o o , / is , ^ , 3 % or 0 . 0 5 5 ; / is 1 ^
13, 411
- 4 ^ p( I r ,|)
T h e f u t u r e v a l u e is $ 1 0 5 0 .
The annual
_ _ .
12 9 3 6 27"
K.4hoi.r!e'<-.,«.(oor-r mil f,e m'rj.ff, $ j 1 gjj.^
after
20 yeais.
T h e compounding period is q u a r t e r i y . o r 4 t i m e s p e r y e a r
T h e t e r m (in y e a r s ) is 1 y e a r ,
^
^
iii) T h e
8 0 4 2 47^
10199 98
^T'
v a l u e is $ 1 0 0 0 .
interest
/6Ci9.ir.
per
T h e a n n u a l interest rate is 4 . 9 4 % .
The annual
4)(1;,
! ^ ' n r . c i p a l ($)^
| Year^ena Valwe j f
i
^ 5090 00 T " ^ ^ :
5243.39
J
T h e t e r m (in y e a r s ) is 1 y e a r .
present
» 5 iO 3 3't •
•
T h e f u t u r e v a l u e is $ 1 0 5 0 ,
ii| The
: y i j , / , c--,^ , ^
5 '-o !.;•.-,,,.•
••
'••
0:o
,'c.,i, i . , „ „ ^ 4 i . , V.400 01 A at, t h e
no./. v,4ue -4 f 4 K
r h n<H/v y e a , U s e a l a b h ; •©
' - m o o , . - 4.',- , i o - . v . . . r . CAmx: v a l u e - , h a v e b e e n
')f!c!S'4 t
r i i e *i|fi,|r. v o l u o c4 If..-; ... .•i-4iOfnt is $ 1 0 5 0 .
b | i | t h f p o - . o m v i ' . K . r^, .31404
h'u: n.'.ntiaf I'liLic J r.jlv >.
niikn^wn.
Tiif- t o n : p o u n U i n y p^ouci lo s e i u i - a n n u a l . o r 2
year.
^
/ » j , 4S..4:, . ,
3 r
times
20"
per year
^
10
.
rPriricij,ali$V
.5275
5000
z z z m i o
6375
_
^
7750
9125
5 0 0 0 _^ _
15500^
B r a d ' s a c c o u n t will h e w o r t h $ 1 0 5 0 0 aHer 2 0
years.
1-13
! i „ > , o i H p . n i u u l o o o« ' " " J 1 . • <-m: ' H n u a l . o r 2
1)1
f ,itl-. IH'.
S i n e - P'-r y<-,)i
: t , f U i U i i i n \-'•<»'•.)
llu'lutulf
i o / i / . I-.
i;v'.-.iiii- r;l
i l i , , h . h i i . - v o l o . <,l I h i - t , . i O 1- > . 0 6 1 , 6 9 , T h i s is
-UKHi
: c-iin
'n
.inknimif
I. ..,', t h . m t h e n o o - n . i i Intn.'.' v,,lo;- )f $ 5 1 7 3 . 2 1
I J__L_|.-l~|——i_i_4—4—4--|
d) lh(
' . nil'I
o o i u ip.)l I . S ioOO
II. ,-.iiutu.il
: . .
I . . ; -
\ ^
|. ,th.'>i,ie's
inti't'-'st
i-th'v
uiiiuMivjn.
l l i e . o , u o < , u n d m o p. r i c d • . 4 ,.lv. o r 3 6 5 t i m e s per y e a r .
1 h e ! o i n i (ill y e . i O . )
IIH
lotoie -oiloe IO $ ' . , ' / • • '
A n loO-ie: t f ; i l e ef S 04'S
;.;)<•<) *
t.-'-e<led tO h a v e 3
i . l t u i e ./.jlO.- •-: 1,1'.'/ '> 31
; -«;.';
5
•, • sf .
I h e pue,, ip.il :s 3 ' . ! '
OOO
P u o . l u i n i a l m t . ' H '.t n i t e r, / /-.'.s
< Ur. , , o i o o < . n n 4 ! n ( j p. n " 4 - , i;-..,idorly, or 4 t i m e s p e r y e a r .
s 000 4
I 4 o l e r m n a -i-v.wA
'',
Ihe tuiuiti vdluv IS
uiiktiuhMi
T h e f u t u r e v a l u e o f t h e i n v e s t m e n t is $ 6 2 9 4 7 . 3 9
^ , n O - " " ' '/.ih>i:
{./...lO-i
6 2 9 4 7 . 3 9 - 50 0 0 0 = 12 9 4 7 3 9
T h e r e will be $ 1 2 9 4 7 . 3 9 available for sports
«.t |!iV0'-4lJ.p-!l { 4 ]
! r.o'j.-'ooe
1 jiiac
5275J
4- >!:•• '
, '
44
'; ^ "
0 ) 0 4 1 4,4
804
4 r '
1!i
<M4.n j
1040'.! I
!
' ' 14"44I3 47
-4»
c ) T h e i n t e r s e c t i o n p o i n t o n t n e g r a p i i n-Oi^ s e e . - , ti
p o i n t a t w h i c h b o t h i n v e s t m e n t s e a r n tt.-
^^n'v..
-m-
S. I n i t i a l I n v e s t m e n t : T h e p n n c i p a i is $ 1 0 0 0 .
T h e a n n u a l i n t e r e s t r a t e is 5 % .
T h e c o m p o u n d i n g p e r i o d is a n n u a l , or o n c e p e r y e a r .
T h e t e r m (in y e a r s ) is 5.
The future value is unknown.
C.OT^^OR
T h e f u t u r e v a l u e of t h e initial i n v e s t m e n t is $ 1 2 7 6 . 2 8 .
O p t i o n A : T h e p n n e i p a l is $ 1 0 5 0 .
of i n t e r e s t .
4 . a) T h e p n n c i p a i is $ 3 0 0 0 .
T h e a n n u a l i n t e r e s t r a t e is 5,6¥o.
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r .
T h e t e r m (in y e a r s ) is 1 0 .
The future value is
unknown.
T h e f u t u r e v a l u e o f t h e G I C is $ 5 1 7 3 . 2 1 .
b) $ 3 0 0 0 will d o u b l e t w i c e t o b e c o m
e g u i p m e n t a t t h e e n d of 3 y e a r s .
T h e a n n u a l i n t e r e s t r a t e is 5 % .
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r .
T h e t e r m (in y e a r s ) is 5.
The future value is
unknown.
T h e f u t u r e v a l u e of o p t i o n A is $ 1 3 4 0 . 1 0 .
O p t i o n B : T h e p n n c i p a i is $ 1 0 0 0 .
»0.
1 ^ x 2 = 25.714...
5 6
It will t a k e a b o u t 2 5 . 7 y e a r s f o r t h e i n v e s t m e n t t o b e
w o r t h at l e a s t $ 1 2 0 0 0 .
c ) i) e g . , If t h e c o m p o u n d i n g f r e g u e n c y i n c r e a s e s t o
m o n t h l y , t h e f u t u r e v a l u e o f t h e i n v e s t m e n t will i n c r e a s e .
T h e a n n u a l i n t e r e s t r a t e is 6 % .
T h e c o m p o u n d i n g p e n o d is a n n u a l , o r o n c e p e r y e a r .
T h e t e r m (in y e a r s ) is 5.
The future value is
unknown.
T h e f u t u r e v a l u e of o p t i o n B is $ 1 3 3 8 . 2 3 .
O p t i o n C : T h e p n n c i p a i is $ 1 0 0 0 .
T h e a n n u a l i n t e r e s t r a t e is 5 % .
T h e c o m p o u n d i n g p e n o d is m o n t h l y , o r 12 t i m e s p e r
M o r e f r e g u e n t c o m p o u n d i n g r e s u l t s in m o r e i n t e r e s t
year.
T h e t e r m (in y e a r s ) is 5.
being earned.
T h e p n n c i p a i is $ 3 0 0 0 ,
T h e a n n u a l i n t e r e s t r a t e is 5 . 6 % ,
T h e f u t u r e v a l u e of t h e o p t i o n C i s $ 1 0 3 , 4 3 6 .
T h e c o m p o u n d i n g p e n o d is m o n t h l y o r 12 t i m e s p e r y e a r .
T h e t e r m (in y e a r s ) is 1 0 .
The future value is
unknown.
T h e f u t u r e v a l u e of t h e G I C is $ 5 2 4 5 . 1 8 . T h i s is m o r e
t h a n t h e o n g i n a l f u t u r e v a l u e of $ $ 5 1 7 3 . 2 1 .
ii) e g . . If t h e i n t e r e s t r a t e c h a n g e d t o 2 . 8 % c o m p o u n d e d
s e m i a n n u a l l y , t h e f u t u r e v a l u e of t h e i n v e s t m e n t w o u l d
d e c r e a s e . A l o w e r i n t e r e s t r a t e m e a n s l e s s i n t e r e s t will
be earned on the investment. T h e c h a n g e f r o m annual to
s e m i - a n n u a l e o m p o u n d i n g will n o t a f f e c t t h e f u t u r e v a l u e
The future
value
is
unknown.
O p t i o n D: T h e p n n c i p a i is $ 1 0 0
T h e a n n u a l i n t e r e s t r a t e is 5 % .
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r .
T h e t e r m (in y e a r s ) is 6.
The future value is
unknown.
a s m u c h a s t h e i n t e r e s t r a t e b e i n g r e d u c e d b y half.
T h e p n n e i p a l is $ 3 0 0 0 .
T h e a n n u a l i n t e r e s t r a t e is 2 . 8 % .
C h a p t e r 1: Financial Mathematics: Investing Money
1-14
•' •
, . ;! ,t
. •: I II • ,"l , 1 . J!
1, , . ,1,
T h e n e w investment has a higher ratio than the
onginal investment.
9. T h e p r i n c i p a l is $ 4 0 0
The annual
interest
rate is
unknown.
T h e c o m p o u n d i n g p e r i o d is m o n t h l y , o r 12 t i m e s p e r
year.
T h e t e r m (in y e a r s ) is 1 0 .
I = '-'l'-':;
I 'T'li'". M _ . r
•H'-tJ'-
/•
i.. 1 . . l . O .
:••"'"'-< •
>'''•
. , - ; . „ .j ..i O^
I . -.0)
h,.
i ,-'.,lo - 0
(•
•. I
,,r.
,(•
.
;T
T h e f u t u r e v a l u e is $ 6 2 5 .
"
T h e a n n u a l i n t e r e s t rate is 4 . 4 7 % .
4, ' i ,r-| I ,
.' , !;,.-
S-
p^,,- i,
1 0 . $ 2 5 0 will d o u b l e t w i c e t o b e c o m e $ 1 0 0 0 .
impact,
7 . a | The present value is
unknown.
The a n n u a l i n t e r e s t rate is 6 % ,
T h e c o m p o o n c i i n g p e r i o d is m o n t h l y , o r 12 t i m e s p e r y e a r
t e r m (in y e a r s ) is 3 y e a r s .
T h e f u t u r e v a l u e is $ 1 0 0 0 0 ,
D e s i r e e s h o u l d i n v e s t $ 8 3 5 6 . 4 5 t o h a v e $ 1 0 0 0 0 in t h r e e
years,
b} The present value is
unknown.
The a n n u a l i n t e r e s t rate is 6 % .
c o m p o u n d i n g p e r i o d is semi^-annyal, o r 2 t i m e s p e r y e a r
t e r m (in y e a r s ) is 3 y e a r s .
T h e f u t u r e v a l u e is $ 1 0 0 0 0 .
D e s i r e e s h o u l d i n v e s t $ 8 3 7 4 . 8 4 t o h a v e $ 1 0 0 0 0 in t h r e e
years.
8. a) 1) The present value is
unknown.
T h e a n n u a l i n t e r e s t rate is 7 . 2 % ,
T h e c o m p o o n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r
T h e t e r m (in y e a r s ) is 2 2 y e a r s .
T h e f u t u r e v a l u e is $ 1 1 0 0 0 .
The ongmal investment was $2382 9 1 .
ii) The present value is
unknown
T h e a n n u a l i n t e r e s t rate is 7 . 2 % ,
T h e c o m p o u n d i n g p e n o d is s e m i - a n n u a l , o r 2 t i m e s p e r y e a r
T h e t e r m (in y e a r s ) is 2 2 y e a r s .
T h e f u t u r e v a l u e is 3 i i K, i.
It will t a k e a b o u t 2 4 y e a r s f o r t h e $ 2 5 0 i n v e s t m e n t
-ow to $ 1 0 0 0 .
p r i n c i p a l is $ 2 5 0 .
a n n u a l i n t e r e s t rate is 6 % .
c o m p o u n d i n g p e r i o d is s e m i - a n n u a l , o r
••oes p e r y e a r .
term (in years) is
unknown.
f u t u r e v a l u e is $ 1 0 0 0 .
It will t a k e 2 3 . 4 5 y e a r s , o r 2 3 . 5 y e a r s f o r t h e $ 2 5 0
investment to g r o w to $ 1 0 0 0 .
L e s s o n 1.5: I n v e s t m e n t s I n v o l v i n g
P a y m e n t s , page 55
Regular
1 . a) T h e r e g u l a r p a y m e n t a m o u n t is $ 2 0 0 .
T h e p a y m e n t f r e g u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r
T h e n u m b e r o f p a y m e n t s is 6 0 0 .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h
payment penod.
T h e a n n u a l i n t e r e s t rate is 4 . 8 % ,
T h e c o m p o u n d i n g f r e g u e n c y is m o n t h l y , o r
12 t i m e s p e r y e a r .
The future
value is
unknown.
T h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 4 9 8 5 2 6 . 6 0 .
b | T h e r e g u l a r p a y m e n t a m o u n t is $ 1 7 5 0 .
T h e p a y m e n t f r e g u e n c y is s e m i - a n n u a l , o r 2 t i m e s
per year.
The ongmal investment was $2320.40.
T h e n u m b e r o f p a y m e n t s is 4 0 ,
b ) T h e ratio w o u l d b e h i g h e r b e c a u s e t h e c o m p o u n d i n g is
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h
more frequent.
payment penod.
T h e p n n c i p a i is $ 1 1 0 0 0 .
T h e a n n u a l i n t e r e s t rate is 5 . 6 % .
T h e a n n u a l i n t e r e s t rate is 7 . 2 % .
T h e c o m p o u n d i n g f r e g u e n c y is s e m i - a n n u a l , o r
T h e c o m p o u n d i n g p e n o d is m o n t h l y , o r 12 t i m e s p e r y e a r
2 times per year.
T h e t e r m (in y e a r s ) is 2 2 y e a r s .
The future
value
is
unknown.
T h e f u t u r e v a l u e o f t h e i n v e s t m e n t is $ 5 3 3 6 5 . 3 8
Original investment:
j.
A ^ 11 0 0 0 . 0 0
P
f
2382.91
= 4,616...
^ ^ 1 1 000.00
' P
232a40"
1 = 4.740.,,
New investment:
A ^ 53 365.38
P
11 0 0 0 . 0 0
^ = 4.851...
F o u n d a t i o n s of M a t h e m a t i c s 12 S o l u t i o n s M a n u a l
The future
value is
unknown.
T h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 1 2 6 1 2 7 3 2
c) T h e r e g u l a r p a y m e n t a m o u n t is $ 5 0 .
T h e p a y m e n t f r e g u e n c y is q u a r t e r i y o r 4 t i m e s p e r y e a r
T h e n u m b e r o f p a y m e n t s is 1 6 0 .
T h e p a y m e n t s are m a d e at the e n d of e a c h
payment period
T h e a n n u a l i n t e r e s t rate is 8 . 4 % ,
T h e c o m p o u n d i n g f r e g u e n c y is g u a r t e d y o r 4 t i m e s
per year.
The future
value is
unknown.
The f u t u r e v a l u e o f t h e i n v e s t m e n t is $ 6 3 8 2 0 , 7 9 ,
d ) T h e r e g u l a r p a y m e n t a m o u n t is $ 5 5 0 0 ,
T h e p a y m e n t f r e q u e n c y is s e m i - a n n u a l , o r 2 t i m e s
per year.
1-13
T h e n u m b e r o f p a y m e n t s is 2 4 ,
T h e p a y m e n t s a r e m a d e at t h e e n d of e a c h p a y m e n t
4. I n v e s t m e n t A will e a r n m o r e i n t e r e s t t h a n
investment B b e c a u s e the $ 5 0 0 0 earns interest for
t h e full f i v e y e a r s w h i l e f o u r $ 1 0 0 0 p a y m e n t s e a r n
period.
T h e a n n u a l i n t e r e s t rate is 6 . 5 % ,
T h e c o m p o u n d i n g f r e q u e n c y is s e m i - a n n u a l , o r 2 t i m e s
interest for less than five years.
I n v e s t m e n t A : T h e p n n c i p a i is $ 5 0 0 0 .
per year.
T f i e future v a l u e is ur^known.
T h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 1 9 5 3 8 9 . 4 7 ,
2 . a) T h e r e g u l a r p a y m e n t a m o u n t is $ 1 0 0 .
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r .
T h e n u m b e r o f p a y m e n t s is 7 2
T h e p a y m e n t s a r e m a d e a t t h e e n d of e a c h p a y m e n t
period.
The annual interest rate is
unknown.
I used the financial application on my calculator: T h e
c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r .
T h e f u t u r e v a l u e is $ 7 8 0 0 . 6 1 .
T h e i n t e r e s t r a t e is 2.683o.
b) The regular payment
amount
is
unknown.
T h e p a y m e n t t r e q u e n c y is s e m i - a n n u a l , o r 2 t i m e s p e r
year.
T h e n u m b e r o f p a y m e n t s is 1 4 .
T h e p a y m e n t s a r e m a d e a t t h e e n d of e a c h p a y m e n t
penod.
T h e a n n u a l i n t e r e s t rate is 3 . 5 % ,
T h e c o m p o u n d i n g f r e q u e n c y is s e m i - a n n u a l , o r 2 t i m e s
T h e f u t u r e v a l u e is $ 3 9 2 7 , 3 8 ,
I used the financial application on my calculator. T h e
p a y m e n t a m o u n t is $ 2 5 0 .
c ) T h e r e g u l a r p a y m e n t a m o u n t is $ 2 0 0 0 0 .
T h e p a y m e n t f r e g u e n c y is q u a r t e r i y o r 4 t i m e s p e r y e a r .
T h e number of payments
is
unknown.
T h e p a y m e n t s a r e m a d e at t h e e n d of e a c h p a y m e n t
period.
T h e a n n u a l i n t e r e s t rate is 4 , 7 5 % .
T h e c o m p o u n d i n g f r e g u e n c y is q u a r t e r t y o r 4 t i m e s p e r
T h e ' f u t u r e v a l u e is $ 1 0 5 4 9 7 0 . 0 1 .
I used the financial application on my calculator: T h e
n u m b e r of p a y m e n t s is 4 1 . 1 9 9 . .. s o t h e t e r m is 1 0 . 3
T h e a n n u a l i n t e r e s t r a t e is 6 % .
T h e c o m p o u n d i n g p e n o d is a n n u a l , or o n c e p e r
year.
T h e t e r m (in y e a r s ) is 5
The future value is
unknown.
T h e f u t u r e v a l u e of i n v e s t m e n t A is $ 6 6 9 1 13.
Interest: 6691.13
5000 = 1691.13
I n v e s t m e n t A e a r n e d $ 1 6 9 1 13 in i n t e r e s t .
I n v e s t m e n t B : T h e r e g u l a r p a y m e n t a m o u n t is
$1000
T h e p a y m e n t f r e g u e n c y is a n n u a l , o r o n c e p e r
year.
T h e n u m b e r of p a y m e n t s is 5.
T h e p a y m e n t s a r e m a d e a t t h e e n d of e a c h
payment penod.
T h e a n n u a l i n t e r e s t rate is 6 % .
T h e c o m p o u n d i n g f r e q u e n c y is a n n u a l , or o n c e p e r
year.
The future value is
unknown.
T h e f u t u r e v a i u e of t h e i n v e s t m e n t is $ 5 6 3 7 . 0 9 .
Interest: 5 6 3 7 . 0 9 - (1000)(5) = 6 3 7 . 0 9
I n v e s t m e n t B e a r n e d $ 6 3 7 . 0 9 in i n t e r e s t .
Investment A earns more interest than
i n v e s t m e n t B.
5. T h e r e g u l a r p a y m e n t a m o u n t is $ 6 0 0 ,
T h e p a y m e n t f r e q u e n c y is q u a r t e r l y o r 4 t i m e s p e r
year.
T h e n u m b e r of p a y m e n t s is 2 0 .
T h e p a y m e n t s a r e m a d e at t h e e n d of e a c h
payment period.
T h e a n n u a l i n t e r e s t r a t e is 8 % .
T h e c o m p o u n d i n g f r e q u e n c y is q u a r t e d y o r 4 t i m e s
per year.
The future value is
unknown.
F r a s e r will h a v e $ 1 4 1 5 0 . 7 7 w h e n h e is 2 1 .
I n t e r e s t : 14 1 5 0 . 7 7 - ( 6 0 0 ) ( 2 0 ) = 2 1 5 0 . 7 7
F r a s e r e a r n e d $ 2 1 5 0 . 7 7 in i n t e r e s t .
years.
3. T h e r e g u l a r p a y m e n t a m o u n t is $ 3 5 0 .
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r .
T h e n u m b e r o f p a y m e n t s is 2 1 6 .
T h e p a y m e n t s a r e m a d e at t h e e n d of e a c h p a y m e n t
period.
T h e a n n u a l i n t e r e s t rate is 7 . 2 % .
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
T h e future value is
unknown.
T h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 1 5 4 0 3 0 . 5 4 ,
Interest: 154 0 3 0 . 5 4 - (216)(350) = 78 4 3 0 . 5 4
D a r i e n e e a r n e d $ 7 8 4 3 0 . 5 4 in i n t e r e s t .
6. The regular payment
amount is
unknown.
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
T h e n u m b e r o f p a y m e n t s is 2 4 ,
T h e p a y m e n t s a r e m a d e a t t h e e n d of e a c h
payment period.
T h e a n n u a l i n t e r e s t rate is 6 % .
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12
times per year.
T h e f u t u r e v a l u e ts $ 5 0 0 0 .
I used the financial application on my calculator:
Z o e y m a d e r e g u l a r d e p o s i t s of $ 1 9 6 . 6 0 .
C h a p t e r 1: F i n a n c i a l M a t h e m a t i c s . I n v e s t i n g M o n e y
1-16
7. a ) i | The regular payment
amount is
unknown.
The p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r .
T h e n u m b e r o f p a y m e n t s is 4 2 0 .
T h e p a y m e n t s are m a d e at the e n d of e a c h p a y m e n t
T h e n u m b e r of p a y m e n t s is 1 2 0 .
penod.
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h
A a r o n : T h e r e g u l a r p a y m e n t a m o u n t is $ 2 5
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s per
year.
T h e a n n u a l i n t e r e s t rate is 1 4 . 6 % .
payment penod.
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
T h e f u t u r e v a l u e is $1 0 0 0 0 0 0 .
J a y n e n e e d s to invest $76 22 at the e n d of each m o n t h .
ii) The regular payment
amount is
unknown.
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r .
T h e n u m b e r o f p a y m e n t s is 4 2 0 .
T h e a n n u a l i n t e r e s t rate is 4 . 2 % .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h p a y m e n t
period.
I ho- a n n u a l i n t e r e s t rate is 6 . 9 % ,
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , c
year.
•
hmes per
T h e f u t u r e v a l u e is $ 1 0 0 0 0 0 0 .
J a y n e n e e d s to i n v e s t $ 5 6 8 . 6 0 at t h e e n d o f e a c h m o n t h ,
b) O p t i o n i):
Interest; 1 0 0 0 0 8 8 . 0 5
Rate of return =
(76.22)(420) = 968 075.65
96807565
3 2 0 1 2 "40
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12
times per year.
The future
value
is
unknown.
A t t h e e n d of f i v e y e a r s , t h e f u t u r e v a l u e of A a r o n ' s
a c c o u n t is $ 3 7 2 0 . 3 3 .
C a s e y : T h e p r e s e n t v a l u e is $ 1 3 5 6 . 1 6 .
T h e a n n u a l i n t e r e s t rate is 4 . 2 % .
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r
year.
T h e t e r m (in y e a r s ) is 10.
The future value is
unknown.
A t t h e e n d o f f i v e y e a r s , t h e f u t u r e v a l u e of C a s e y ' s
a c c o u n t is $ 2 0 4 6 . 3 9 .
A a r o n ' s i n v e s t m e n t is w o r t h m o r e t h a n C a s e y ' s
investment.
O p t i o n i) rate o f r e t u r n is 3 0 2 4 . 0 6 % .
9. T h e r e g u l a r p a y m e n t a m o u n t is $ 5 0 0 .
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
O p t i o n ii):
T h e n u m b e r o f p a y m e n t s is 6 0 ,
Rate of return = 30.240 6 4 5 , , .
Interest: 1 0 0 0 008.39 - (568.60)(420) = 761 196.39
R a t e of r e t u r n =
761196.39
'23"8812
R a t e of r e t u r n = 3 . 1 8 7 4 2 9 . , .
O p t i o n ii) rate o f r e t u r n is 3 1 8 . 7 4 % ,
J a y n e s h o u l d c h o o s e o p t i o n i) s i n c e t h e rate o f r e t u r n is
a l m o s t t e n t i m e s g r e a t e r t h a n t h e rate of r e t u r n f o r o p t i o n
ii).
8. a ) T h e r e g u l a r p a y m e n t a m o u n t is $ 2 5
T h e p a y m e n t f r e q u e n c y is m o n t h l y , or 12 t i m e s per y e a r .
T h e n u m b e r o f p a y m e n t s is 6 0 .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h p a y m e n t
period.
T h e a n n u a l i n t e r e s t rate is 4 . 2 % ,
T h e c o m p o u n d i n g f r e g u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
The future value is
unknown.
A t t h e e n d of f i v e y e a r s , t h e f u t u r e v a l u e of A a r o n s
a c c o u n t is $ 1 6 6 5 . 9 0 .
b) The present value is
unknown.
T h e a n n u a l i n t e r e s t rate is 4 . 2 % .
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r .
T h e t e r m (in y e a r s ) is 5.
T h e f u t u r e v a l u e is $ 1 6 6 5 . 9 0 .
T h e p r e s e n t v a l u e is $ 1 3 4 8 . 0 2 .
Casey invested $1356.16.
c ) A a r o n ' s i n v e s t m e n t will b e w o r t h m o r e at t h e e n d o f
10 y e a r s b e c a u s e h e is m a k i n g m o r e f r e g u e n t d e p o s i t s
a n d t h e i n t e r e s t is c o m p o u n d e d m o r e o f t e n .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h
payment penod.
The annual
interest
rate is
unknown.
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12
times per year.
T h e f u t u r e v a l u e is $ 3 5 0 0 0 ,
I used the financial application on my calculator:
T h e a n n u a l i n t e r e s t rate is 6 . 1 3 % .
1 0 . T h e r e g u l a r p a y m e n t a m o u n t is $ 1 0 0 0 .
T h e p a y m e n t f r e g u e n c y is s e m i - a n n u a l , o r 2 t i m e s
per y e a r .
The number of payments
is
unknown.
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h
payment penod.
T h e a n n u a l i n t e r e s t rate is 7 . 5 % .
T h e c o m p o u n d i n g f r e g u e n c y is s e m i - a n n u a l , o r
twice per year.
T h e f u t u r e v a l u e is $ 1 0 0 0 0 .
I u s e d t h e f i n a n c i a l a p p l i c a t i o n o n m y c a l c u l a t o r : It
will t a k e 8 . 6 5 p a y m e n t s o r 4 . 3 3 y e a r s f o r t h e
i n v e s t m e n t to b e w o r t h a t least $ 1 0 0 0 0 .
11. D e e : T h e r e g u l a r p a y m e n t a m o u n t is $ 1 0 0 0 .
T h e p a y m e n t f r e g u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r .
T h e n u m b e r o f p a y m e n t s is 6 0 .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h p a y m e n t
period.
T h e a n n u a l i n t e r e s t rate is 4 % .
T h e c o m p o u n d i n g f r e g u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
The future
value
is
unknown.
A t t h e e n d of f i v e y e a r s , t h e f u t u r e v a l u e o f D e e ' s
a c c o u n t is $ 6 6 2 9 8 . 9 8 .
F o u n d a t i o n s o f M a t h e m a t i c s 12 S o l u t i o n s M a n u a l
1-17
Pete:
H»e li-.jtii.i! (s.ivH'etil n i n i . i i n ! i .
I hi-p.ivineni trfi|Ufiiev
K H ' i i i h S v er 1
e
ti>fn,-, p e r y e a r ,
i lit- .niMiher of [ . . i v m e n l - . r. h-'fi
J h.- p a y i n e i i ! - , a t e f i i e h . - a l l l i e .-nh el i-a» |. p , r y m e n t
Oen-.xl
I ti< . i i i i i e a l int«,'ie-.l i a l e r. 1' '..
I h e e . n i i p e u f i l i n q !i»;(]uent y i'- r:>i »fih)|-v , . H W ii'v-es p e r
year.
The Mure
value is
unknown.
A t t h e e n d o f t e n y e a r s , t h e f u t u r e v a l u e of P e t e ' s
a c c o u n t is $ 7 3 6 2 4 . 9 0 .
b ) T h e f u t u r e v a l u e of P e t e ' s i n v e s t m e n t is h i g h e r t h a n
14. a ) J i l l : The regular
payment
amount
is
unknown.
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
T h e n u m b e r of p a y m e n t s is 3 6 0 .
T h e p a y m e n t s a r e m a d e at t h e e n d of e a c h
payment period.
T h e a n n u a l i n t e r e s t rate lo ' - l " - - .
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , or 12
t i m e s per year.
T h e f u t u r e v a l u e is $ 2 5 0 0 0 0 .
Jill n e e d s t o i n v e s t $ 1 8 9 2 9 at t h e e n d of e a c h
Dee's investment because each deposit Pete m a d e had
month
m o r e time to a c c u m u l a t e interest, a n d additional interest
$ 1 8 9 . 2 9 - 3 6 0 = 168 144.40
w a s paid on the a c c o m u l a t e d interest,
V a u g h n : The regular
1 2 . T r e y : T h e r e g u l a r p a y m e n t a m o u n t is $ 6 0 0 .
unknown.
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
payment
amount
is
T h e n u m b e r o f p a y m e n t s is 8.
T h e p a y m e n t s are m a d e at the e n d of e a c h p a y m e n t
year.
T h e n u m b e r o f p a y m e n t s is 3 6 0 .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h
period.
T h e a n n u a l i n t e r e s t r a t e is 3 . 6 % .
T h e c o m p o u n d i n g f r e q u e n c y is q u a r t e r l y or 4 t i m e s p e r
payment period.
T h e a n n u a l i n t e r e s t r a t e is 1 1 . 6 % .
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12
year.
The Mure
value is
unknown.
A t t h e e n d of t w o y e a r s , t h e f u t u r e v a l u e of T r e y ' s
times per year.
T h e p a y m e n t f r e q u e n c y is q u a r t e r l y o r 4 t i m e s p e r y e a r .
T h e f u t u r e v a l u e is $ 2 5 0 0 0 0
V a u g h n n e e d s t o i n v e s t $ 7 8 . 1 6 a t t h e e n d of e a c h
month
a c c o u n t is $ 4 9 5 3 . 9 5 ,
S a m : T h e r e g u l a r p a y m e n t a m o u n t is $ 2 4 0 0 ,
$ 7 3 00
T h e p a y m e n t f r e q u e n c y is a n n u a l , o r o n c e p e r y e a r .
$6.1 ' ''A .10 - $ 2 8 1 3 7 . 6 0 = $ 4 0 0 0 6 . 8 0
T h e n u m b e r o f p a y m e n t s is 2 ,
Jill I , e < i , t o i n v e s t $ 4 0 0 0 6 . 8 0 m o r e t h a n V a u g h n
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h p a y m e n t
period.
T h e a n n u a l i n t e r e s t r a t e is 3 . 8 % ,
T h e c o m p o u n d i n g f r e q u e n c y is a n n u a l , o r o n c e p e r y e a r .
The future value Is
unknown.
A t t h e e n d o f t w o y e a r s , t h e f u t u r e v a l u e of S a m ' s
a c c o u n t is $ 4 8 9 T 2 0 ,
Difference: 4953,95, - 4 8 9 T 2 0 = 62.75
0 = 28 137.60
ov> ' l o e 3 0 y e a r s .
b) , ^.o' r e g u l a r p a y m e n t a m o u n t is $ 1 8 9 . 2 9 ,
T h e p a y m e n t f r e q u e n c y is m o n t h l y , or 12 t i m e s p e r
year.
T h e n u m b e r of p a y m e n t s is 3 6 0 ,
T h e p a y m e n t s a r e m a d e a t t h e e n d of e a c h
payment period.
T r e y ' s i n v e s t m e n t is w o r t h $ 6 2 . 7 5 m o r e t h a n S a m ' s
T h e a n n u a l i n t e r e s t r a t e is 1 1 . 6 % .
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12
investment.
times per year.
13. Total price of e n t e r t a i n m e n t s y s t e m :
V a u g h n will h a v e $ 6 0 5 5 0 1 . 1 9 a t t h e e n d of
(2499){T13) = 2823.87
T h e r e g u l a r p a y m e n t a m o u n t is $ 2 2 5 .
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r .
30 years
T h e n u m b e r of p a y m e n t s is 12.
T h e p a y m e n t f r e q u e n c y is w e e k l y , o r 5 2 t i m e s p e r
T h e p a y m e n t s a r e m a d e at t h e e n d of e a c h p a y m e n t
year.
T h e n u m b e r o f p a y m e n t s is 1 0 4 .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h
The future
period.
T h e a n n u a l i n t e r e s t r a t e is 3 . 6 % .
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
The future value is
unknown.
In o n e y e a r . M i g u e l ' s a c c o u n t will b e w o r t h $ 2 7 4 5 . 0 0 .
$2745.00 - $2823.87 = -
$78.87
M i g u e l will b e s h o r t $ 7 8 . 8 7 .
value
is
unknown.
15. T h e r e g u l a r p a y m e n t a m o u n t is $ 3 0 0 .
payment penod.
T h e a n n u a l i n t e r e s t r a t e is 1 0 . 5 % .
T h e c o m p o u n d i n g f r e q u e n c y is w e e k l y , o r 5 2 t i m e s
per year.
T h e future
value
is
unknown.
T i m w i l l h a v e $ 3 4 6 7 9 . 0 8 a t t h e e n d of t w o y e a r s .
W i t h t h e $ 5 0 0 0 0 h e g e t s f r o m s e l l i n g his first
sailboat, he has $84 679.08.
Difference: 120 000 - 84 679.08 = 35 320.92
T i m will n o t h a v e e n o u g h m o n e y t o b u y his d r e a m
sailboat. He needs an additional $35 320.92. assuming
t h e s a i l b o a t ' s p n c e h a s n o t i n c r e a s e d in t h e t w o y e a r s .
1-18
C h a p t e i 1- h m a n c i a l M a t h e m a t i c s : I n v e s t i n g M o n e y
16. a )
T h e a n n u a l i n t e r e s t r a t e is 3 . 6 % .
Similar
Different
B o t h h a v e a t o t a l p r i n c i p a l of
$1200.
O p t i o n A IS a
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12
times per year.
single deposit
T h e f u t u r e v a l u e is $ 3 7 5 0 .
Both earn 6 % annual interest
while option B
I used the financial application on my calculator:
compounded monthly.
is a s e r i e s of
B ^ l i a r e i n v e s t e d for 10 y e a r s .
payments.
Farah n e e d s to deposit $ 1 5 0 . 9 3 at the e n d of e a c h
m o n t h in o r d e r t o b u y a n e w c o m p u t e r in t w o
years.
b)
Opfjo^i A
Olio
p,-. i -o
_
_ I Cjptioo B
|_ (1 o ' ' ' f i - ' i u i . • a n .
i
i l l ^H'< ri'.)u.l>
I
"
1 i . R e g u l a r payment investment: The regular
p a y m e n t a m o u n t is $ 5 0 .
T h e p a y m e n t f r e q u e n c y is s e m i - a n n o a l . o r 2 t i m e s
per year.
per A n n u m
T h e n u m b e r o f p a y m e n t s is 4 0 .
.f r'
i
T h e p a y m e n t s are m a d e at the e n d of e a c h
payment period.
s
iOi.-n
T h e a n n u a l i n t e r e s t r a t e is 5 % .
T h e c o m p o u n d i n g f r e q u e n c y is s e m i - a n n u a l , o r 2
S40 n , 3 ^
; ' o; O.
The future
-o 0 /
1
times per year.
/'g 2 9
I
loia/g^
value
is
unknown.
T h e v a l u e o f t h e a c c o u n t a f t e r 2 0 y e a r s is
$3370.13.
L u m p s u m i n v e s t m e n t : T h e p n n c i p a i is
$3370.13.
T h e a n n u a l i n t e r e s t r a t e is 5 % ,
25(
T h e c o m p o u n d i n g p e r i o d is s e m i ^ a n n o a L o r 2
times per year.
investment A
investment B
T h e t e r m (in y e a r s ) is 10 y e a r s .
The future
value
is
unknown.
T h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 5 3 3 6 5 . 3 8
T h e final v a l u e of t h e i n v e s t m e n t is $ 5 5 2 2 . 3 5 .
i t l J
2©. A m o u n t n e e d e d : 4 6 0 0 0 ( 1 . 0 5 ) ^ 4 0 0 0 = 4 4 3 0 0
T h e r e g u l a r p a y m e n t a m o u n t is $ 5 5 0 .
f.S . It
T h e p a y m e n t f r e g u e n c y is m o n t h l y , o r 12 t i m e s p e r
Time
1
J-.'l-'j-i o f hiVt=,..:)tiorif (.;>,
t iptpo
f'
Opt:ori B
0
1200
2 — p i;.92
4~" - L j t ) 2 4
'i9
6
40
1/19
- 4
10
year.
'i'.r
204
t2
349
03
T h e n u m b e r o f p a y m e n t s is 6 0 .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h
payment period.
T h e a n n u a l i n t e r e s t rate is 9 , 8 % .
301^09
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12
1 9 3 0 97 ^ " ~
1323 2 9 "
times per year.
'.-'I/O' 23^'^ "
lb
18
7o
1 h e v a l u e of ( ) p t i o n tJ g r o w s rnuoii t a s t e r t h a n t h e v a l u e
o f O p t i o n A , but m u c h o f O p t i o n B's g r o w t h is d u e to t h e
monthly deposits. Option A earns more interest than
o p t i o n B o v e r t h e 10 y e a r s .
The future
value
is
unknown.
In f i v e y e a r s . P a t ' s a c c o u n t will b e w o r t h
$ 4 2 3 6 6 . 0 1 , P a t n e e d s t o s a v e $ 4 4 3 0 0 to a f f o r d
t h e car, s o h e c a n n o t m a k e t h e p u r c h a s e
be short by $1933,99,
P a t will
1 7 . N o . e . g . , T h e p r o b a b i l i t y t h a t his t i p s will e q u a l t h e
s a m e a m o u n t e a c h m o n t h is v e r y u n l i k e l y . ( H o w e v e r , t h e
problem could be solved using the formula
A = R+R(1+
if + R ( 1 + if + ... +
+ ,|n^1 a n d
c h a n g i n g R to t h e v a l u e F a r a h d e p o s i t s e a c h m o n t h . )
18. A m o u n t n e e d e d : 5000 - 5000(0.25) = 3750
F a r a h will n e e d $ 3 7 5 0 in h e r a c c o u n t a f t e r t w o y e a r s .
The regular
payment
amount
is
unknown.
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r
T h e n u m b e r o f p a y m e n t s is 2 4 .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h p a y m e n t
period.
F o y n d a t i o n s o f M a t h e m a t i c s 12 S o l y t i o n s M a n u a l
1-19
M a t h i n A c t i o n , p a g e 5S
. e . g . . t h e i n t e r e s t r a t e f o r a 5^year G I C is 1 . 2 6 7 % p e r
a n n u m , a n d t h e i n t e r e s t r a t e f o r a 5 - y e a r m o r t g a g e is
5.19%, compounded semi-annually.
. T h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 5 4 2 3 0 . 3 8 6 . . . or
$ 5 4 2 3 0 . 3 9 , a n d t h e i n t e r e s t e a r n e d is $ 4 2 3 0 . 3 9 .
CSB:
I tir imncipul
o.
!inkn.'wt<
I l i e o n i u i o l iot<.'io;,l mto- r- (7'.,
f h e . . o i i i p o u n d i n g p e n o d ••- - • n o o o l , nr on'X- p.a y.>at
I l u ! t ( ' n n (in y o o r s ) m 2 y e a r s
I h u l u h i i u vo'i.io IO $ 4 . 3 3 . i 0 ; t
; >r,biii a n d I frslie s p a u ' t t h . -,l-'Olld (Jivi: tp.-ir. $4(143
h'
. T h e future value of the m o r t g a g e (with no regular loan
p a y m e n t s ) is $ 6 4 5 9 9 , 9 1 7 . . . o r $ 6 4 5 9 9 9 2 . a n d t h e
i n t e r e s t c h a r g e d is $ 1 4 5 9 9 , 9 2 ,
3. C S B s
ZZZJ
Year
. T h e difference b e t w e e n the interest paid by the bank
1
1000
a n d t h e i n t e r e s t e a r n e d b y t h e b a n k is $ 1 0 3 6 9 , 5 3 . w h i c h
y
looo
represents the a m o u n t earned by the bank,
,)
. T h e greater the difference between the a m o u n t of
interest that a bank pays on an investment and the
a m o u n t of i n t e r e s t t h a t t h e b a n k c h a r g e s o n a l o a n , t h e
m o r e m o n e y t h e b a n k will m a k e .
L e s s o n 1.6: S o l v i n g I n v e s t m e n t
Problems, page
4
5
t)
/
Portfolio
64
8
9
0,0.^.4
f) 0 3 1
_^ 0
1 0 0 0 3- 0 f l
,
0,034
1
00 ' 3 . U a 4
100(^ 0 0 3 4
_
a c c o u n t w o u l d allow him to e a r n interest on his w e e k l y
savings.
b) G I C : T h e p n n c i p a i is $ 3 0 0 .
T h e a n n u a l i n t e r e s t r a t e is 5 % .
T h e c o m p o u n d i n g p e n o d is a n n u a l , o r o n c e p e r y e a r .
T h e t e r m (in y e a r s ) is 1 y e a r .
The future value is
unknown.
T h e G I C will b e w o r t h $ 3 1 5 a t t h e e n d of o n e y e a r .
S a v i n g s a c c o u n t : T h e r e g u l a r p a y m e n t a m o u n t is $ 1 5 .
T h e p a y m e n t f r e q u e n c y is w e e k l y , or 5 2 t i m e s p e r y e a r .
T h e n u m b e r o f p a y m e n t s is 5 2 .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h p a y m e n t p e r i o d .
T h e a n n u a l i n t e r e s t r a t e is 2 . 9 % .
T h e c o m p o u n d i n g f r e q u e n c y is w e e k l y , or 5 2 t i m e s p e r y e a r .
The
future
value
is
unknown.
T h e s a v i n g s a c c o u n t will b e w o r t h $ 7 9 1 . 2 0 at t h e e n d o f o n e
I he c3;>Bs a i e w n h h $ 1
_
n/7
\v.\\
^
m a
'
119'.!
I Z Z l l Z Z Z I Z I l l l
" "
i "
1000
_
p o'7
100C i P 0 3 4
,
1222
ior,;!'
0 (TA
^hiOl
1263
j_
1. a) A G I C w o u l d a l l o w S t a n t o e a r n i n t e r e s t o n t h e $ 3 0 0
he has f r o m his s u m m e r job. T h e high interest savings
1 ,i31
130t,
,)0 0 9 3 4
Tooo 6 0 3 4
00
A($)
n
4-:
T r u s t a c c o u n t . T n o p r i n c i p a l is $oOOO.
T h e a n n u a l i n t e r e s t r a t e is 4 . 3 % .
T h e c o m p o u n d i n g p e n o d is q u a r t e d y , o r 4 t i m e s p e r
year.
T h e t e r m (in y e a r s ) is 4 2 y e a r s .
The future value is
unknown.
T h e t r u s t a c c o u n t is w o r t h $ 1 8 0 8 3 . 0 3 .
G I C : T h e p n n c i p a i is $ 1 0 0 0 0
T h e a n n u a l i n t e r e s t r a t e is 3 . 9 5 % .
T h e c o m p o u n d i n g p e n o d is s e m i - a n n u a l , or 2 t i m e s p e r
ygar.
T h e t e r m (in y e a r s ) is 10 y e a r s .
The future value is
unknown.
T h e G I C is w o r t h $ 1 4 7 8 6 . 8 0 .
T o t a l : 11 6 7 7 . 3 2 + 18 0 8 3 . 0 3 + 1 4 7 8 6 . 8 0 = 4 4 5 4 7 . 1 5
year.
F i v e - y e a r b o n d : T h e p n n c i p a i is $ 4 4 5 4 7 . 1 5
Total s a v e d : 315 + 791.20 = 1106 20
Difference: 1750
1106.20 = 643.80
S t a n will n o t h a v e e n o u g h m o n e y in o n e y e a r t o b u y t h e
guitar. He n e e d s $ 6 4 3 . 8 0 more.
The regular payment
amount is
unknown.
T h e p a y m e n t f r e q u e n c y is w e e k l y , o r 5 2 t i m e s p e r y e a r .
T h e n u m b e r o f p a y m e n t s is 5 2 .
T h e a n n u a l i n t e r e s t r a t e is 5 . 1 % .
T h e c o m p o u n d i n g p e n o d is a n n u a l , o r o n c e p e r y e a r .
T h e p a y m e n t s a r e m a d e at t h e e n d of e a c h p a y m e n t p e n o d .
is $ 5 0 .
T h e p a y m e n t f r e q u e n c y is m o n t h l y , or 12 t i m e s p e r y e a r .
T h e a n n u a l i n t e r e s t r a t e is 2 . 9 % .
T h e c o m p o u n d i n g f r e q u e n c y is w e e k l y , o r 5 2 t i m e s p e r y e a r ,
S t a n n e e d s t o d e p o s i t $ 2 7 . 2 1 into his a c c o u n t e a c h w e e k t o
m e e t his g o a l .
2
I n v e s t m e n t a c c o u n t : T h e r e g u l a r p a y m e n t a m o u n t is $ 5 0 .
T h e p a y m e n t f r e q u e n c y is w e e k l y , o r 5 2 t i m e s p e r y e a r .
T h e t e r m (in y e a r s ) is 5 y e a r s .
The future value is
unknown.
T h e f i v e - y e a r b o n d will b e w o r t h $ 5 7 1 2 5 . 9 6 .
4. a ) I n v e s t m e n t a c c o u n t : T h e r e g u l a r p a y m e n t a m o u n t
T h e n u m b e r of p a y m e n t s is 3 6 .
T h e p a y m e n t s are m a d e at the e n d of e a c h p a y m e n t
period.
T h e a n n u a l i n t e r e s t r a t e is 2 . 7 % .
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
T h e c o m p o u n d i n g f r e q u e n c y is w e e k l y , or 5 2 t i m e s p e r y e a r .
year.
The future value is
unknown.
T h e i n v e s t m e n t a c c o u n t is w o r t h $ 1 8 7 2 . 7 2 .
R E S P a c c o u n t : T h e r e g u l a r p a y m e n t a m o u n t is $ 1 0 .
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r .
Ttie future value is
unknown.
T h e s a v i n g s a c c o u n t will b e w o r t h $ 5 4 1 6 . 9 2 at t h e e n d of t w o
T h e n u m b e r o f p a y m e n t s is 2 1 6 .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h p a y m e n t
T h e n u m b e r of p a y m e n t s is 1 0 4 .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h p a y m e n t p e r i o d .
T h e a n n u a l i n t e r e s t r a t e is 4 . 1 % ,
D W e r e n c e : 10 0 0 0 - 5 4 1 6 . 9 2 = 4 5 8 3 , 0 8
R o b i n a n d L e s l i e n e e d a n a d d i t i o n a l $ 4 5 8 3 . 0 8 in t w o y e a r s .
1-20
period.
T h e a n n u a l i n t e r e s t rate is 3 . 2 % .
C h a p t e r 1: F i n a n c i a l M a t h e m a t i c s : I n v e s t i n g M o n e y
T h e cofTipouncling f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
The future
value is
4
<4C
i
unknown
b | Gayla has the greater savings because her m o n e y
h a s b e e n i n v e s t e d f o r 12 y e a r s l o n g e r t h a n C o r e y ' s
money.
Gayla: Regular payment investment:
lie r e g u l a r p a y m e n t a m o u n t is $ 1 5 .
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r
n u m b e r o f p a y m e n t s is 1 4 4 .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h p a y m e n t
period
a n n u a l i n t e r e s t rate is 3 . 6 % .
T h e c o m p o u n d i n g f r e g u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
The future
value is
unknown.
T h e i n v e s t m e n t is w o r t h $ 2 6 9 6 . 7 0 .
L u m p s u m i n v e s t m e n t : T h e p n n c i p a i is $ 2 6 9 6 70
T h e a n n u a l i n t e r e s t rate is 3 . 8 % .
T h e c o m p o u n d i n g p e r i o d m o n t h l y , o r 12 t i m e s p e r y e a r
T h e t e r m (in y e a r s ) is 10 y e a r .
The future
value is
unknown.
I't'- '• I
i
al, or 2 times per
1 y e a r s ) is 10
f a / o e is unknc
,v -.n- , o , 0 ,
4SB-.
•Of
T h e c o m p o u n d i n g p e n o d is daily, o r 3 6 5 t i m e s p e r y e a r
T h e t e r m (in y e a r s ) is 1 y e a r .
The future value is
unknown.
5. a) G a y l a ' s p r i n c i p a l : ( 1 5 ) ( 1 2 ) ( 1 2 ) = 2 1 6 0
Corey pnncipai: (18)(12)(10) = 2160
They both invested $2160.
I
il
P a u l a h a s $ 4 7 8 8 . 5 1 w h e n s h e s t a r t s first y e a r .
b) Difference: 4788.51 ^ 2000 = 2788.51
T h e p r i n c i p a l is $ 2 7 8 8 . 5 1
T h e a n n u a l m t e r e s t rate is 3 , 5 % ,
T h e c o m p o u n d i n g p e n o d is d a i l y , o r 3 6 5 t i m e s p e r y e a r
T h e t e r m (in y e a r s ) is 1 year.
The future value is
unknown.
T h e s a v i n g s a c c o u n t is w o r t h $ 9 1 9 4 5 a f t e r o n e y e a r .
A m o u n t s h o r t : 2 0 0 0 - 9 1 9 . 4 5 = 1 0 8 0 55
P a u l a will n o t h a v e e n o u g h m o n e y s a v e d for t h i r d y e a r
S h e n e e d s to save $ 1 0 8 0 . 5 5 over the s u m m e r .
3- 0
HI p< .1 'I •< , | r « ; [ II >i I- • I
I ••• '
T h e R E S P a c c o u n t is w o r t h $ 2 9 1 5 . 7 9 .
Total; 1872.72 + 2915.79 = 4788.51
T h e s a v i n g s a c c o u n t is w o r t h $ 2 8 8 7 . 8 3 a f t e r o n e y e a r .
P a u l a will h a v e e n o u g h m o n e y s a v e d for s e c o n d y e a r
c| D i f f e r e n c e : 2 8 8 7 8 3 ^ 2 0 0 0 = 8 8 7 8 3
T h e p r i n c i p a l is $ 8 8 7 8 3
T h e a n n u a l i n t e r e s t rate is 3 , 5 % .
'
iO-:•(-•-• (f-'cr,- -.1
1
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1 .
1 h;oo
. O o m
1000
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i
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S
1
:
:
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1
i
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, s ; y 1 f: •
! o ij-'o
j 1
1
1
~
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I.OOM
t :»
",}•
If
- •'" " •
1
3,'3:;
I
T h e C S B ; i a r e w o r t h !i ' / O S
•
d.-f p.syaK o t io
The
(I p,'./((
a m o u n t is ; t S O ; ,
;o4'joo
—
ostment:
ice per year,
'',1.''
• "1
./.;•,'. I
'ach p a y m e n t
I n e a n n u a l i n t e r e s t r a t e is 5 % .
'• ' •
• I'Ti
'
" ' ! . • ' • w 4,/! I
i-.-:-.>:-v,,,
I H". '.liof [,• . , J./ Of.
':•>•'. Ol, { .• v-.i,'::
,
,
or once per year.
', , / 0-3.
L y . t i p s y m i n v e s t m e n t : 1 n e p r i n c i p a l is $ 1 6 5 3 2 9 8
T h e a n n u a l i n t e r e s t r a t e is 5 % .
The
The
The
The
c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r
t e r m (in y e a r s ) is 2 0 y e a r s .
future value is
unknown.
t r u s t a c c o u n t is w o r t h $ 4 3 8 6 6 . 9 1 .
T o t a l ; 15 4 5 3 . 1 8 + 5 7 5 8 , 1 4 + 4 3 8 6 6 . 9 1 = 6 5 0 7 8 . 2 3
J a y n e ' s i n v e s t m e n t p o r t f o l i o is w o r t h $ 6 5 0 7 8 2 3
P r i n c i p a l : 10 0 0 0 + 1 0 0 0 ( 5 ) + 5 0 0 ( 2 0 ) = 2 5 0 0 0
Interest; 6 5 0 7 8 . 2 3 - 2 5 0 0 0 = 4 0 0 7 8 . 2 3
R a t e of r e t u r n = i i O Z 8 : 2 3
25 000
R a t e of r e t u r n = 1 6 0 3 , .
J a y n e ' s rate o f r e t u r n o n h e r i n v e s t m e n t is 1 6 0 . 3 % .
7. a) S a v i n g s a c c o u n t : T h e r e g u l a r p a y m e n t a m o u n t
is $ 5 0 .
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
G a y l e ' s t o t a l i n v e s t m e n t is w o r t h $ 3 9 4 0 . 9 7 .
T h e n u m b e r o f p a y m e n t s is 2 4 0 .
C o r e y : T h e r e g u l a r p a y m e n t a m o u n t is $ 1 8 .
T h e p a y m e n t s a r e m a d e at t h e e n d of e a c h p a y m e n t
T h e p a y m e n t f r e g u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r .
T h e n u m b e r o f p a y m e n t s is 1 2 0 .
T h e a n n u a l i n t e r e s t rate is 2 . 7 % .
T h e p a y m e n t s a r e m a d e at t h e e n d of e a c h p a y m e n t
period.
T h e a n n u a l i n t e r e s t rate is 3 . 8 % .
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
The future
value is
unknown.
C o r e y ' s i n v e s t m e n t is w o r t h $ 2 6 2 2 . 7 3 ,
Gayle has a larger investment than Corey,
penod.
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12 t i m e s
per year.
The future
value is
unknown.
W h e n Ela is f o r t y , t h e s a v i n g s a c c o u n t is w o r t h
$15 888.14.
F i r s t 1 0 - y e a r G I C : T h e p n n c i p a i is $ 1 5 8 8 8 . 1 4
T h e a n n u a l i n t e r e s t rate is 4 . 2 % .
T h e c o m p o u n d i n g p e n o d is m o n t h l y , o r 12 t i m e s p e r
year.
T h e t e r m (in y e a r s ) is 10 y e a r s .
The future value is
unknown.
W h e n Ela is fifty, t h e G I C is w o r t h $ 2 4 1 6 3 . 4 1
F o u n d a t i o n s o f M a t h e m a t i c s 12 S o l u t i o n s M a n u a l
1-21
S e c o n d 1 © - f e a r G I C : T h e p r i n c i p a l is $ 2 4 1 6 3 . 4 T
T h e a n n u a l i n t e r e s t r a t e is 4 . 3 % .
T h e c o m p o u n d i n g p e r i o d is m o n t h l y , or 12 t i m e s p e r
value
is
unknown.
T h e a n n u a l i n t e r e s t r a t e is 3 . 9 % .
! h'> It.'on o n y o . i r o i;. K ) y u o r - .
iiituii-
v.ihir
T h e c o m p o u n d i n g p e n o d is w e e k l y , or 5 2 t i m e s p e r
unktumu
y V l i c u 1 i l i-. ^.i^3y, I h o t 4 i ; i s w t ; r t l i $ ' /
i 13 t}5.
F i r s t 1 0 - y e a r b o i i d : I h t ; p n o f i p n l is $ 5 0 0 .
I h i ; H o n n . i l intun,"..! l o l u i s 3 P r X ,
1 p.: . . u i u p D u o d i i K i o-Hind i s a n n u a l , o r o n c e p e r y e a r .
ill. - litUut:
\/uH:n i ;
y ' 4 i f ; n r i a I- fifiv, tin- t i o n d v. w r j f l l i $ 7 3 3 . 0 4 .
S e c o n d l O ^ y e o r b o n d : 1 l u ; o n n c i p a l is $ 7 3 3 . 0 4 .
; he . l o n i i . i l in1c>o-,t l o l i : IS 3 ' } ' 3 -
1 h f '.offii.rtiund'Hq p i s ' f K l r. o n u u a i , o r o n c e p e r y e a r .
in: I ire value
is
yooro
unknown.
y y h i . n i i a is s i x t y , t h e b o n d is w o r t h $ 1 0 7 4 . 6 9 .
U.lti
I 116.85 + 1 0 7 4 . 6 9 = 3 8 1 9 1 . 5 4
W h e n Ela t u m s s i x t y , t h e t o t a l value of his p o r t f o l i o is
$ 3 8 191 5 4 .
h) P r i n c i p a l : 5 0 ( 2 4 0 ) + 5 0 ' >
Interest: 38 191.54
T h e t e r m (in y e a r s ) is 10 y e a r s .
The future value is
unknown.
T h e s a v i n g s a c c o u n t is w o r t h $ 5 3 7 2 . 4 7 .
O p t i o n A will b e w o r t h $ 2 7 7 9 0 . 5 6 in t e n y e a r s .
iniknrmn
; h; i<H,,! (!fi v^Nir .) IS
ys3r
Total: 22 418.09 + 5372.47 = 27 792.04
! h t ' l»?ini (10 y t j . i i s ) r . 10 y r a r s
; h'
The future
T h e G I C IS w o r t h $ 2 2 4 18 0 9 .
S a v i n g s a c c o u n t : T h e p n n e i p a l is $ 3 6 3 8 .
vear.
llu-
T h e t e r m (in y e a r s ) is 10 y e a r s .
T sOO
12 5 0 0 - ' 3 6 9 1 . 5 4
2 5 691.6-1
O p t i o n B : T h e p n n e i p a l is $ 1 8 6 3 8 .
T h e a n n u a l i n t e r e s t r a t e is 3 . 9 % .
T h e c o m p o u n d i n g p e n o d is d a i l y , o r 3 6 5 t i m e s p e r
ygar.
T h e t e r m (in y e a r s ) is 10 y e a r s .
The future value is
unknown.
O p t i o n B will b e w o r t h $ 2 7 5 2 7 . 3 9 in t e n y e a r s .
O p t i o n A is w o r t h $ 2 6 3 . 1 7 m o r e t h a n o p t i o n B.
Derek should chose option A.
10. e . g . . A n i n v e s t m e n t p o r t f o l i o m a y c o n s i s t of
single p a y m e n t i n v e s t m e n t s or regular p a y m e n t
i n v e s t m e n t s . S o m e i n v e s t m e n t s m a y l o c k in f u n d s
f o r a p e r i o d of t i m e l i m i t i n g a c c e s s t o it b u t o f t e n
- 4e of return
offer a higher interest rate. Investments offenng a
r o s e of r e t u r n = 2 . 0 5 5 . . .
s r a t e o r r e t u r n o n his i n v e s t m e n t is 2 0 5 . 5 % .
lower interest rate usually allow a c c e s s to the
funds. A higher investment amount usually tends
to offer higher interest rates. T h e greater the
8. a) C o s t of t n p : 2 0 0 0 + 3 0 0 ( 1 2 ) = 5 6 0 0
pnncipai, t e r m , interest rate, and c o m p o u n d i n g
T h e p n n e i p a l is $ 1 2 0 0 .
f r e q u e n c y , t h e f a s t e r t h e i n v e s t m e n t will g r o w .
T h e a n n u a l i n t e r e s t r a t e is 5%o.
T h e c o m p o u n d i n g p e n o d is a n n u a l , or o n c e p e r y e a r .
1 1 . 3 ) B e t t y h a s $ 2 0 0 0 0 0 n o w . s o t h i s is t h e
T h e t e r m (in y e a r s ) is 4 y e a r s .
p r e s e n t v a l u e . S h e will h a v e n o m o n e y in t h e
The future
a c c o u n t in t e n y e a r s , s o t h e f u t u r e v a l u e is z e r o .
value
is
unknown.
T h e G I C is w o r t h $ 1 4 5 8 . 6 1 a t maturity.
S o l v e for t h e r e g u l a r p a y m e n t a m o u n t .
Difference: 5600 ^ 1458.61 = 4141,39
The regular
N o , J o will n o t h a v e e n o u g h m o n e y for h e r t n p in f o u r
T h e p r e s e n t v a l u e is $ 2 0 0 0 0 0 .
y e a r s . S h e will b e $ 4 1 4 1 . 3 9 s h o r t ,
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
b) If s h e m a k e s w e e k l y d e p o s i t s f o r f o u r y e a r s , t h a t is
yggf
2 0 8 deposits. Divide the a m o u n t s h e needs to have by
T h e n u m b e r of p a y m e n t s is 1 2 0 .
208.
T h e p a y m e n t s a r e m a d e a t t h e e n d of e a c h
4141.39
- = 19.910.
208
e . g . , I e s t i m a t e t h a t J o w i l l n e e d t o m a k e d e p o s i t s of a n
payment
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12
times per year.
T h e f u t u r e v a l u e is 0.
is
unknown.
unknown.
payment period.
The regular
amount
is
T h e a n n u a l i n t e r e s t r a t e is 5 % .
a m o u n t less than $ 1 9 91 to m e e t her g o a l .
payment
amount
T h e p a y m e n t f r e g u e n c y is w e e k l y , or 5 2 t i m e s p e r y e a r .
I used the financial application on my calculator:
T h e n u m b e r of p a y m e n t s is 2 0 8 .
T h e p a y m e n t s a r e m a d e at t h e e n d of e a c h p a y m e n t
B e t t y will r e c e i v e 1 2 0 m o n t h l y p a y m e n t s of
period.
T h e a n n u a l i n t e r e s t r a t e is 2 . 3 % .
T h e c o m p o u n d i n g f r e q u e n c y is w e e k l y , or 5 2 t i m e s p e r
year.
T h e f u t u r e v a l u e is $ 4 1 4 1 . 3 9 .
J o n e e d s t o m a k e w e e k l y d e p o s i t s of $ 1 9 . 0 1 t o m e e t h e r
goal.
9. O p t i o n A : G I C : T h e p r i n c i p a l is $ 1 5 0 0 0 .
T h e a n n u a l i n t e r e s t r a t e is 4 . 1 % .
T h e c o m p o u n d i n g p e r i o d is a n n u a l , or o n c e p e r y e a r .
1-22
$2121.31.
b) The regular
payment
amount
is
unknown.
T h e p r e s e n t v a l u e is $ 2 0 0 0 0 0 .
T h e p a y m e n t f r e q u e n c y is m o n t h l y , or 12 t i m e s p e r
year
T h e n u m b e r o f p a y m e n t s is 1 2 0 .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h
payment penod.
T h e a n n u a l i n t e r e s t r a t e is 7 . 5 % .
T h e c o m p o u n d i n g f r e g u e n c y is m o n t h l y , o r 12
times per year.
T h e f u t u r e v a l u e is 0.
C h a p t e r 1: F i n a n c i a l M a t h e m a t i c s : I n v e s t i n g M o n e y
I used the financial application on my calcylator; Betty
w o u l d r e c e i v e 1 2 0 m o n t h l y p a y m e n t s of $ 2 3 7 4 , 0 4 if t h e
i n t e r e s t rate i n c r e a s e d to 7 , 5 % .
12. Regular payment investment: The regular payment
a m o u n t is $ 1 5 0 ,
T h e p a y m e n t f r e q u e n c y is a n n u a l , o r o n c e p e r y e a r .
T h e n u m b e r o f p a y m e n t s is 5 0 .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h p a y m e n t
period.
Tfie term (in years) is
unknown.
T h e f u t u r e v a l u e is $ 5 0 0 0 0 ,
I used the financial application on my calcylator;
T h e o p t i o n B i n v e s t m e n t will g r o w t o $ 5 0 0 0 0 in
112.64 periods or 28.16 years.
V a l s h o u l d c h o o s e o p t i o n A b e c a u s e s h e will r e a c h
her financial goal about 4 years sooner.
3
."4 I
!.,„,•
• •' • , ' ».
0/ O'p.l
(..
T h e a n n u a l i n t e r e s t rate is 8 . 8 % .
' o
it o i . i ,1 p . i v ( i i « ' ( H .j!u
T h e c o m p o u n d i n g f r e q u e n c y is a n n u a l , o r o n c e p e r y e a r .
'
r n''n= - c
Tfie future
value is
}
•( f! 3 O'O' <
,
I i-ii :
yo,
j . n ar v'' ^ < !'»n!--i,-, o r 12 t i m e s p e r
unknown.
T h e i n v e s t m e n t is w o r
320,88,
M o n t h l y I n c o m e : The regular
payment
iber o f p a y m e n t s is 2 4 0 ,
amount
is
unknown.
Tients a r e m a d e at t h e e n d o f e a c h
.period,
.,....
T h e p r e s e n t v a l u e is $ 1 1 3 9 2 0 , 8 8 ,
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r .
T h e n u m b e r o f p a y m e n t s is 1 2 0 ,
T h e p a y m e n t s are m a d e at the e n d of e a c h p a y m e n t
period.
T h e a n n u a l i n t e r e s t rate is 4 , 8 % .
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
T h e f u t u r e v a l u e is 0.
I used the financial application on my calculator: Sty's
g r a n d m o t h e r will r e c e i v e 1 2 0 m o n t h l y p a y m e n t s o f
$ 1 1 9 7 . 2 0 . S h e will r e c e i v e $ 1 4 3 6 6 4 . 0 0 a l t o g e t h e r in
payments.
a n n u a l i n t e r e s t rate is 5 . 8 % .
T h e e o m p o u n d i n g f r e g u e n c y is m o n t h l y , o r 12
times per year.
The future
value
is
unknown.
W a r r e n ' s i n v e s t m e n t is c u r r e n t l y w o r t h $ 2 2 5 6 . 2 4
Interest; 2 2 5 6 . 2 4 ^ 1200 = 1056,24
R a t e of r e t u r n = 1 0 5 6 2 4
1200,00
R a t e of r e t u r n = 0 . 8 8 0 , , ,
W a r r e n ' s rate o f r e t u r n o n his i n v e s t m e n t is 8 8 % .
b | W a r r e n i n v e s t e d a t o t a l ., ; /• i< - ' tie m a d e
m o n t h l y d e p o s i t s f o r five y e a r s , e a c h d e p o s i t v^ould
be:
Chapter Self-Test, page 68
1
•
-S'
6
r>
f h e i.nvo^iri,-..! will d o u b l e in a b o u t 12 y e a r s
T h e p r i n c i p a l is $ 4 0 0 0 0 .
T h e a n n u a l i n t e r e s t rate is 633.
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r .
The term (in years) is
unknown.
T h e f u t u r e v a l u e is $ 8 0 0 0 0 .
I used the financial application on m y calculator; Hal's
i n v e s t m e n t will d o u b l e in 11.9 y e a r s
b}A = P + Prt
A is $ 8 0 0 0 0 ; P is $ 4 0 0 0 0 ; ris 6 % o r 0 . 0 6
80 000 = 4 0 000 + (40 000)(0.06)(f)
40 000 = 2400f
t= 1 6 . 6 6 6 . . .
W i t h s i m p l e interest, H a l ' s i n v e s t m e n t wili d o u b l e in
16.67 years.
(5)(12)
r e g u l a r p a y m e n t a m o u n t is $ 2 0 .
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
T h e n u m b e r o f p a y m e n t s is 6 0 ,
T h e p a y m e n t s are m a d e at the e n d of each
payment penod.
T h e a n n u a l i n t e r e s t rate is 5 . 8 % .
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12
times per year.
The future
value is
unknown.
Warren's investment would be currently worth
$1388.25.
c| The regular payment
amount is
unknown.
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
year
T h e n u m b e r o f p a y m e n t s is 6 0 .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h
2 . O p t i o n A : T h e p r i n c i p a l i^ 3 i 3 9 0 0 .
payment period.
T h e a n n u a l i n t e r e s t rate is 6 % .
T h e a n n u a l i n t e r e s t rate is 5 . 8 % .
T h e c o m p o u n d i n g p e r i o d is s e m i - a n n u a l , o r 2 t i m e s p e r
T h e e o m p o u n d i n g f r e g u e n c y is m o n t h l y , o r 12
times per year.
The term (in years) is
unknown.
T h e f u t u r e v a l u e is $ 5 0 0 0 0 .
I used the financial application on my calculator; The
o p t i o n A i n v e s t m e n t will g r o w t o $ 5 0 0 0 0 in 4 8 . 2 8 p e r i o d s
or 24.14 years.
O p t i o n B : T h e p r i n c i p a l is $ 1 2 0 0 0 ,
T h e a n n u a l i n t e r e s t rate is 5 , 1 % .
T h e c o m p o u n d i n g p e r i o d is q u a r t e r t y , o r 4 t i m e s p e r
year.
F o u n d a t i o n s of M a t h e m a t i c s 1? S o l u t i o n s M a n u a l
T h e f u t u r e v a l u e is $ 2 2 5 6 . 2 4 .
I used the financial application on m y calculator:
W a r r e n w o u l d have n e e d e d to m a k e monthly
p a y m e n t s of $32.50.
4 . a) A l e x : G I C : T h e p n n c i p a i is $ 5 0 0 0 .
T h e a n n u a l i n t e r e s t rate is 2 . 6 % .
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r
year.
1-23
• l l , - I c i r . i f i . i \ii
I III-
Itlt'lli
K/.iliH-
i:,
.<l>
Chapter Review, paye 71
|»n!i; iM-il r . $'/fH)iJ
Itw
s
than Jamie does.
>Ulkll()Wn
I t|.> < 4 i . I-. W u . l l l
CSB-
Alex h a s a greater rate of return o n his portfolio
.1? , | i< ' } v ' - ' i ' ' -
rinu.it i n t . - ! c s l r.itt- i s
1. a ) A = P +
i 1
;..-nii ,i.;ini.il,
t i « - . { . i . i p u u i i . j m c j f f i s ' - t i I'
or 2 times per
Prt
A is $ 2 8 5 0 ; P i s $ 1 5 0 0 ; r i s 6
2850 = 1500 + (1500)(rj(6)
yf>,lf
I p r !<ir(i OM ys- H ' I
; / } . . f,,lh(t'
Wih.f
i:
J
1350=OOOOr
y^'Uts
lirih'H
f=0,15
nvi!
T h e C S B earned a n annual interest rate of 1 5 % ,
Its.- i . S B IS w u U h $-0^'f,1 PH',
S a v i n g s a r c o i i r i t . 1 fi»- i s t i u l o . ' o . i y m e i i t a m o u n t is $ 1 5 .
11,.- 0 . 0 / 0 . ' I'.: i:* oo.;ii< / I S w c r P l y
I :,<"
.lOOii.J f u; |».i./'ii.-!;ls r
o,.. ,,,.y.ps-..-
oi
o
times per year.
'I
eacti payment
period.'
T h e a n n u a l i n t e r e s t r a t e is 1.4%.
T h e c o m p o u n d i n g f r e q u e n c y is w e e k l y , o r 5 2 t i m e s p e r
year.
The future
a n n u a l l y s o t h e a m o u n t will b e t h e s a m e w h e t h e r
s h e r e d e e m s t h e C S B w h e n s h e is 18 or 18 a n d a
/Of-
.",!" . s . i p . . ..i l o u
b) T n s h w o u l d g e t $ 2 8 5 0 , T h e i n t e r e s t is p a i d
halt
2.JO
V : i n c lf,.Aj%f
value
is
unknown.
Z
! i 4 ( ; ! o s l ! labs p s .
T h e a c c o u n t is w o r t h $ 4 0 3 9 . 1 8 .
/\OUUI i
T o t a l ; 6 2 9 9 . 3 6 + 2 2 6 1 . 8 8 + 4 0 3 9 . 1 8 = 12 6 0 0 . 4 2
•.' 4ii'.'
_
tl r o d
T h e t o t a l v a l u e o f A l e x ' s p o r t f o l i o is $ 1 2 6 0 0 . 4 2 .
GIC
CSB
10 0 0 0
7(410
o on '
0.114
J_
.f«vir
i o 0 iO (!{•
r
1
' a m i e : B o n d : A = P ( 1 + rt)
,
//no, oo
: 1 ;i90 UP ;
o ; 4 ) i fK»
$ 3 0 0 0 ; f is 2 . 7 % o r 0 . 0 2 7 ; t is 9
3000(1 + (0.027)(9))
3729
I h e b o n d is w o r t h $ 3 7 2 9 .
CS3:
•4
I
~*
11
T h e p r i n c i p a l is $ 7 0 0 .
1>--.0''";4'
i n 9 9 0 PK;
dUfuO
13 3 _ 8 t s 0 0
I
o, b/OjlO
i
1
P i 1 8 2 OU
o.ttjOOO
• 0(3
OS O i o ' i K
• a n n u a l i n t e r e s t r a t e is 2 . 8 % ,
4if5 c o m p o u n d i n g p e r i o d is s e m i - a n n u a l , o r 2 t i m e s p e r
year.
13 y ^ ' u i s
t h e • <)(,.
C4B i S v L 4 h 3 l :
T h e t e r m (in y e a r s ) is 3 y e a r s .
The
/Otof
future
value
is
I V S N I U .3 O i ' o o u o u t h e
3/4
b)
Comparisons of
Investments
unknown.
T h e C S B is w o r t h $ 7 6 0 . 9 0 ,
S a v i n g s a c c o u n t : T h e r e g u l a r p a y m e n t a m o u n t is $ 1 0 0 .
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r .
18 One
T h e n u m b e r o f p a y m e n t s is 7 2 .
The payments a r e m a d e at t h e e n d of each payment
16 ono
penod.
T h e a n n u a l i n t e r e s t r a t e is 1,7%,
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
The future
value
is
unknown.
T h e a c c o u n t is w o r t h $ 7 5 7 4 , 3 7 .
T o t a l - 3 7 2 9 + 7 6 0 . 9 0 + 7 5 7 4 . 3 7 = 12 0 6 4 . 2 7
2
14C'L''J
1
12 0SU
2
10 000
Grandmother's
GIC
i
Grandfathers
CSB
n. -0
3
s 000
T h e t o t a l v a l u e o f J a m i e ' s p o r t f o l i o is $ 1 2 0 6 4 . 2 7 .
1 uon
b) A l e x :
2 000
P r i n c i p a l ; 5 0 0 0 + 2 0 0 0 + 1 5 ( 5 2 ) ( 5 ) = 10 9 0 0
e
Interest; 12 6 0 0 . 4 2 ^ 10 9 0 0 = 1700.42
5
6
Years
1700.42
R a t e of r e t u r n
Rate of return = 0.156...
A l e x ' s r a t e o f r e t u r n o n h i s i n v e s t m e n t is 1 5 . 6 % .
P r ^ d p a l ; 3 0 0 0 + 7 0 0 + 1 0 0 ( 1 2 ) ( 6 ) = 10 9 0 0
I n t e r e s t ; 12 0 6 4 . 2 7 - 10 9 0 0 = 1 1 6 4 . 2 7
1164.27
Rateofretun.-
^ - ^
R a t e of r e t u r n = 0 . 1 0 6 8 . ..
J a m i e ' s rate o f r e t u r n o n h e r i n v e s t m e n t is 1 0 . 7 % .
1-24
Time
V a l u e of Investment ($) ^
lynaibi
GIC
j : S B ^
1
10 6 3 0 , 0 0
7798.00
~3
11 8 9 0 . 0 0
9394 00
" 5
"
~7
13 1 5 0 , 0 0
00
•
.0.00
6.00
15 6 7 0 , 0 0
2 00
1 1
16 9 3 0 . 0 0
15 778 0 0
lo""
18 1 9 0 . 0 0
17 3 7 4 . 0 0
Chapter 1 l-ioancial Mathematics: Investing Money
re i n t e r e s t is i n c r e a s i n g in
Johnny;
T h e C S B will s o o n b e w o r t h
R a t e of r e t u r n =
'
•*""•' •
••' ••Oil h a v e t h e g r e a t e s t r e t u r n
'
-
•• • '
over a short time.
1-9 S o t O . J
'
•
/:
f.'-' Simple interest investments
m p o u n d interest investments
894.71
2000 00
R a t e of r e t u r n = 0 . 4 4 7
J o h n n y ' s r a t e o f r e t u r n is 4 4 . 7 % .
J o h n n y ' s r a t e o f r e t u r n is h i g h e r t h a n J a m e s ' s rate
of return.
f • )
• • '•462;f!s5
, i i l l ! . , « • . • . , . . ( , ' , . . ..
5. T h e p n n c i p a i is $ 9 0 0 ,
The annual
interest
rate is
unknown.
T h e c o m p o u n d i n g p e r i o d is d a i l y , o r 3 6 5 t i m e s p e r
year.
T h e t e r m (in y e a r s ) is 1 y e a r .
T h e f u t u r e v a l u e is $ 1 0 0 0 .
I u s e d the financial application o n m y calculatorKyle's a n n u a l interest rate w a s 1 0 . 5 4 % .
1r*'j4
. = F f l + f)"
r = 5.3% compounded monthly
-
1 1 6 . . . ; f = S y e a r s . 11 = 6 0
1 + 0.0
-M'
.f°
34
605 34 ^ 2000 = 605.34
R a t e of r e t u m =
T h e c o m p o u n d i n g p e n o d is s e m i - a n n u a l , or 2
times per year.
T h e t e r m (in y e a r s ) is 18 y e a r s .
T h e f u t u r e v a l u e is $ 1 2 5 0 0 0 .
Phil i n v e s t e d a p n n e i p a l o f $ 3 9 5 2 4 . 6 3 .
2000 00
Rate of return = 0.3026...
T r e n t ' s r a t e of r e t u m is 3 0 . 3 % .
Sonia has a slightly higher rate of return than Trent d o e s
c | S o m a ' s investment earned more interest b e c a u s e the
a n n u a l interest rate w a s higher a n d the t e r m w a s too
s h o r t for t h e c o m p o u n d i n g o f i n t e r e s t in T r e n t ' s a c c o u n t
to be noticeable.
4 . a ) J o h n n y will e a r n m o r e i n t e r e s t b e c a u s e t h e i n t e r e s t
o n his a c c o u n t is c o m p o u n d e d m o r e f r e q u e n t l y
J a m e s : T h e p r i n c i p a l is $ 2 0 0 0 .
T h e a n n u a l m t e r e s t rate is 7 . 4 % .
T h e c o m p o u n d i n g p e r i o d is s e m i - a n n u a l , o r 2 t i m e s p e r
year.
f f t e r m (in y e a r s ) is 5 y e a r s .
The future value is
unknown.
J a m e s ' s i n v e s t m e n t is w o r t h $ 2 8 7 6 . 1 9 .
Interest; 2 8 7 6 . 1 9 - 2 0 0 0 = 8 7 6 . 1 9
J a m e s e a r n e d $ 8 7 6 . 1 9 in i n t e r e s t ,
J o h n n y : T h e p n n c i p a i is $ 2 0 0 0 .
T h e a n n u a l i n t e r e s t r a t e is 7 . 4 % .
T h e c o m p o u n d i n g p e n o d is w e e k l y , o r 5 2 t i m e s p e r y e a r
T h e t e r m (in y e a r s ) is 5 y e a r s .
The future value is
unknown.
J o h n n y ' s i n v e s t m e n t is w o r t h $ 2 8 9 4 7 1
Interest; 2894.71 ^ 2 0 0 0 = 894.71
J o h n n y e a r n e d $ 8 9 4 . 7 1 in i n t e r e s t .
J o h n n y ' s investment earned m o r e interest than J a m e s ' s
did
b) J a m e s :
Rate of return
6- a ) P h i l : The principal
is
unknown.
T h e a n n u a l i n t e r e s t rate is 6 . 5 % .
= i Z 6 J l
2000.00
L i n a : The principal
is
unknown.
T h e a n n u a l i n t e r e s t rate is 6 . 5 % .
T h e c o m p o u n d i n g p e n o d is s e m i - a n n u a l , o r 2
times per year
T h e t e r m (in y e a r s ) is 3 6 y e a r s .
T h e f u t u r e v a l u e is $ 1 2 5 0 0 0 .
L i n a i n v e s t e d a p n n c i p a i of 3 1 ' 4 ' - 7 . 5 7
39 524.6 .
> ' \:>f
= 21 0 2 7 . 0 6
Phil i n v e s t e d $ 2 7 0 2 7 . 0 6 m o r e t h a n L i n a d i d
b) T h e p n n c i p a i is $ 3 9 5 2 4 . 6 3 .
T h e a n n u a l i n t e r e s t rate is 6 . 5 % .
T h e c o m p o u n d i n g p e r i o d is s e m i - a n n u a l , o r 2
times per year.
T h e t e r m (in y e a r s ) is 3 6 y e a r s .
The future
value is
unknown.
L i n a w o u l d h a v e $ 3 9 5 3 2 3 . 0 7 in h e r a c c o u n t a f t e r
36 years.
T a ) Mel: The principal
is
unknown.
T h e a n n u a l i n t e r e s t r a t e is 6 . 5 % .
T h e c o m p o u n d i n g p e r i o d is a n n u a l , or o n c e p e r
year.
T h e t e r m (in y e a r s ) is 10 y e a r s .
T h e f u t u r e v a l u e is $ 1 3 1 4 0 .
Mel invested a pnncipai of $7000.02
M i k e : The pnncipai
is
unknown.
T h e a n n u a l i n t e r e s t r a t e is 9 . 6 % .
T h e c o m p o u n d i n g p e r i o d is m o n t h l y , o r 12 t i m e s
per year.
T h e t e r m (in y e a r s ) is 10 y e a r s .
T h e f u t u r e v a l u e is $ 1 3 0 0 9 .
M i k e i n v e s t e d a p n n c i p a i of $ 5 0 0 0 . 1 2 .
M e l i n v e s t e d m o r e p r i n c i p a l 10 y e a r s a g o .
R a t e of r e t u r n = 0 . 4 3 8 . ..
J a m e s ' s r a t e o f r e t u r n is 4 3 . 8 % .
F o u n d a t i o n s o f M a t h e m a t i c s 12 S o l u t i o n s M a n u a l
1-25
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 1 2
| j | f , a l ( . i i l , i l = - fl>«- H i v i - . t u . i ' u t V O I I H ; ; . t : V « y I w n
^ Piincipal
Mo!
Miko
/ocioo,'
h o n i ) 1.-'
($)
'\ I n t e r e s t R a t e
per
I Coiii|JOunding
vc:ir.
i
times per year.
The Mure value is
unknown.
B a n k B a c c o u n t is w o r t h $ 8 2 1 3 9 , 0 3 .
Difference: 8 4 319.81
8 2 139 0 3 = 2 1 8 0 . 7 8
]
M a r y will h a v e $ 2 1 8 0 , 7 8 m o r e if s h e c h o o s e s
A n n u m
oniiuul
period
i inonttily
bank A,
' V a l u e at E n d o f Y e a r
;
7fj:iO (to
4 0 ! 74 .':./
79
V444V_n
T h e p a y m e n t f r e q u e n c y is a n n u a l , o r o n c e p e r
10714
"44741X0
1 i d f d i fio
1 O . M 0 oo
10/44
year.
T h e n u m b e r o f p a y m e n t s is 4 5 .
The payments are m a d e at the end of each
0001)
"
f.OOO 14
/ o o o n?
i . a ) J o s h : T h e r e g u l a r p a y m e n t a m o u n t is $ 1 0 0 0 .
O
13fM)4 0 1
payment period.
T h e a n n u a l i n t e r e s t r a t e is 634.
T h e c o m p o o n d i n g f r e q u e n c y is a n n u a l , o r o n c e p e r
,fi)|j..ii
\<:;^--\:-' 111
ygar.
The Mure value is
unknown.
J o s h ' s i n v e s t m e n t is w o r t h $ 2 1 2 7 4 3 . 5 1 .
J e f f : T h e r e g u l a r p a y m e n t a m o u n t is $ 3 0 0 0 .
T h e p a y m e n t f r e g u e n c y is a n n u a l , o r o n c e p e r
13
1
12 0 0 0
1
4~
000
yggf
1 0 ;( n
Mel
9 an
T h e n u m b e r o f p a y m e n t s is 1 5 .
The payments are made at the end of each
i ;
4
payment period.
T h e a n n u a l i n t e r e s t r a t e is 6 % .
T h e c o m p o u n d i n g f r e q u e n c y is a n n u a l , o r o n c e p e r
7 •11)') j
f
0 0 0 1
year.
The future
4
000
value
is
unknown.
J e f f s i n v e s t m e n t is w o r t h $ 6 9 8 2 7 . 9 1
b) Josh: 1000(45) = 4 5 000
Jeff; 3 0 0 0 ( 1 5 ) - 4 5 0 0 0
They both invested $45 000.
\/a!u(r(4 lfivostn)fnt^(3p
Time
c ) J o s h 3 1 . ' 7 4 3 . 5 1 •• 4 5 0 0 0 = 1 6 7 7 4 3 . 5 1
/OOOO?
i
7049.Wi I
z m
6
:i ^
in"
c) e . g . ,
'
Jeff; 6 9 8 2 7 . 9 1 - 4 5 0 0 0 = 2 4 8 2 7 , 9 1
ZIMoo-'i'
^
oOOh 4 0 "
" f 1485 0 0
10744 4 4 _
I " ^
' 1 4 1 4 0 0 0 {_ _
1 3009 0 \
mvesoment
will
investment. Mike's investment e a r n s more
steeper and more
8.
B a n k A :
T h e
The
of
interest
a n d isc o m p o u n d e d m o r e frequently, s ot h eg r a p h
is
regular payment amount
is $ 8 0 0 .
p a y m e n t f r e q u e n c y is m o n t h l y , o r 1 2 t i m e s p e r
year.
p a y m e n t s a r e m a d e a t t h e end of e a c h
is
unknown.
payment penod.
T h e a n n u a l i n t e r e s t r a t e is 6 % .
T h e c o m p o u n d i n g f r e q u e n c y is a n n u a l , o r o n c e p e r
T h e ' f u t u r e v a l u e is $ 2 1 2 7 4 3 , 5 1 ,
I used the financial application o n m y calculator;
Jeff w o u l d n e e d t o deposit $ 9 1 4 0 , 0 5 every year for
15 y e a r s t o h a v e t h e s a m e f i n a l v a l u e a s J o s h .
payment
1 0 . a ) It is difficult t o p r e d i c t w h o will b e a b l e t o
period.
T h e
amount
curved.
T h e n u m b e r o f p a y m e n t s is 7 2 .
T h e
payment
T h e p a y m e n t f r e q u e n c y is a n n u a l , o r o n c e p e r
year.
T h e n u m b e r o f p a y m e n t s is 1 5 .
The payments are made at the end of each
b e c o m e l a r g e r and g r o w f a s t e r t h a n t h e tutun.. v a l u e
Mel's
d ) The regular
Oct74 ' 4 | ^
; " "
of y i k e ' s
e a r n e d $ 2 4 8 2 7 . 9 1 in i n t e r e s t .
P*^9iIIL
" 07414 O i
Ttie future value
J o s h e a r n e d $ 1 6 7 7 4 3 . 5 1 in i n t e r e s t a n d J e f f
AQ.53._8Z._.
annual interest rate
p u r c h a s e t h e m o r e e x p e n s i v e c a r in f i v e y e a r s
is 1 2 . 2 % .
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 1 2 t i m e s
per
because the monthly deposit amounts and
c o m p o u n d i n g rates are very similar. D r e w deposits
yesr.
The Mure
value
is
B a n k A a c c o u n t is
B a n k
$ 2 0 0 per m o n t h total a n d has interest c o m p o u n d e d
unknown.
w o r t h $84 319.81.
B : T h e regular payment amount
b i w e e k l y . J o h n d e p o s i t s a slightly h i g h e r m o n t h l y
a m o u n t , $ 2 1 7 . a n d h i s i n t e r e s t is c o m p o u n d e d
is $ 8 0 0 .
T h e
p a y m e n t f r e q u e n c y i s m o n t h l y , or 12 t i m e s per
T h e
n u m b e r of p a y m e n t s i s 72.
T h e
p a y m e n t s a r e m a d e a t t h e e n d of e a c h
year.
slightly less frequently (monthly).
payment
period.
T h e
annual interest rate
is 1 1 . 4 % .
Chapter 1 ( I
1-26
lancial
Mathematics: Investing Money
b | D r e w : T h e r e g u l a r p a y m e n t a m o u n t is $ 1 0 0 ,
T h e p a y m e n t f r e q u e n c y is b i w e e k l y , o r 2 6 t i m e s p e r
year.
^liMJ^MMol
T h e n u m b e r o f p a y m e n t s is 1 3 0 ,
T h e p a y m e n t s are m a d e at the e n d of e a c h p a y m e n t
penod.
T h e a n n u a l i n t e r e s t rate is 4 , 8 % ,
T h e c o m p o u n d i n g f r e q u e n c y is b i w e e k l y , o r 2 6 t i m e s p e r
year.
The future
value is
unknown.
h.,tf,-. , .,r,-.:P . tMture v a l u e .
^ 2 r t f M ! O l _
-!OU Ch,
_ _
! Portfolio 2
_ _
j in!i->.,'.l
I />.uiH,)i .!. i„r
, 1>'3»)u
ri„.>,ipr
'
jP. ,.,
I .<!• H.,y f .r-.,o<,iii„f.,io
>, III ; , • . - , !
3 o n . ! uuii.;„l
depositsof
31 .-oo
'-annyai
I f,..,r.}wrii.cfin
D r e w wili h a v e $ 1 4 6 7 7 . 4 3 in f i v e y e a r s .
J ..'.h if,v.. . i l l , ' ) , h r i . s o f . i i / l l . , . Interest t h a t is
John:
• .,..ip<.ii'i4. .: n n o 3<-t|M0 .t!/ 1} -.r the
'
' ' 0 ' ' ' - 0 ' n 4 p o r l i o l i u 1 j.o'o^.o.oi.c
b) P o r t f o l i o 1:
G I C : T h e p r i n c i p a l is $ 2 5 0 0 0 .
T h e a n n u a l i n t e r e s t rate is 8 . 7 % .
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r
year.
T h e r e g u l a r p a y m e n t a m o u n t is $ 2 1 7 .
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r
T h e n u m b e r o f p a y m e n t s is 6 0 .
T h e p a y m e n t s are m a d e at the e n d of e a c h p a y m e n t
period.
T h e a n n u a l i n t e r e s t rate is 4 . 8 % .
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
year
The future
value is
unknown.
J o h n will h a v e $ 1 4 6 8 2 . 2 6 in f i v e y e a r s ,
J o h n wiil b e a b l e t o p u r c h a s e a m o r e e x p e n s i v e car.
1 1 . a | i| R e g u l a r d e p o s i t i n v e s t m e n t : The regular
p a y m e n t a m o u n t is $ 4 5 0 .
T h e p a y m e n t f r e q u e n c y is q u a r t e r i y . o r 4 t i m e s p e r y e a r
T h e n u m b e r o f p a y m e n t s is 4 0 .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h p a y m e n t
period.
T h e a n n u a l i n t e r e s t rate is 4 , 5 % .
T h e t e r m (in y e a r s ) is 10 y e a r s ,
f o r e value is
unknown.
T h e CSIC is w o r t h $ 5 7 5 7 5 . 2 0 ,
CSB.
n i . rt)
P is $4 0 0 0 0 ; r i s 6 . 4 % o r 0 , 0 6 4 ; f is 10
4 = 4 ; 000(1 +(0,064)(10))
30
. is w o r t h $ 1 6 4 0 0
investment: The regular payment
^m .'.sl ts $ 2 5 0 0 ,
T h e p a y m e n t f r e g u e n c y is a n n u a l , o r o n c e p e r y e a r .
T h e n u m b e r o f p a y m e n t s is 10.
T h e p a y m e n t s a r e m a d e at t h e e n d of e a c h p a y m e n t
period.
T h e c o m p o u n d i n g f r e q u e n c y is q u a r t e r l y , o r 4 t i m e s p e r
year.
The future value is
unknown.
T h e a n n u a l i n t e r e s t rate is 4 . 9 % .
T h e s a v i n g s a c c o u n t is w o r t h $ 2 2 5 7 5 , 0 7 ,
T h e c o m p o u n d i n g f r e q u e n c y is a n n u a l , o r o n c e p e r y e a r
L u m p s u m i n v e s t m e n t : T h e p n n c i p a i is $ 5 0 0 0 ,
The future
T h e a n n u a l i n t e r e s t rate is 6 % .
T h e i n v e s t m e n t is w o r t h $ 3 1 2 9 8 3 5 .
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r
T o t a l : 5 7 5 7 5 2 0 + 16 4 0 0 + 31 2 9 8 . 3 5 = 105 2 7 3 5 5
P o r t f o l i o 1 is w o r t h $ 1 0 5 2 7 3 . 5 5
Portfolio 2:
T h e t e r m (in y e a r s ) is 10 y e a r s .
The future
value is
unknown.
T h e t r u s t a c c o u n t is w o r t h $ 8 9 5 4 . 2 4 .
Total: 22 575.07 + 8954.24 = 31 529.31
T h e v a l u e o f C h a n d r a ' s p o r t f o l i o is $ 3 1 5 2 9 3 1
ii) P r i n c i p a l : 4 5 0 ( 4 0 ) + 5 0 0 0 = 2 3 0 0 0
I n t e r e s t : 31 5 2 9 . 3 1 ^ 2 3 0 0 0 = 8 5 2 9 . 3 1
R a t e of r e t u r n = ^ ^ 2 a 3 1
23 000
Rate of return = 0.3708...
C h a n d r a ' s rate of return is 3 7 . 1 % .
b ) N o , s h e will not h a v e e n o u g h f o r 4 y e a r s
31 5 2 9 . 3 1 - 10 0 0 0 = 21 5 2 9 . 3 1
$ 2 1 5 2 9 . 3 1 i n v e s t e d for 1 y e a r at 6 . 2 % c o m p o u n d e d
annually g r o w s to $22 864.13,
2 2 8 6 4 , 1 3 - ^ 10 0 0 0 = 12 8 6 4 . 1 3
$ 1 2 8 6 4 . 1 3 i n v e s t e d for 1 y e a r at 6 . 2 % c o m p o u n d e d
a n n u a l l y g r o w s to $ 1 3 6 6 1 . 7 1 ,
value
is
unknown.
G I C : T h e p n n c i p a i is $ 2 5 0 0 0 .
T h e a n n u a l i n t e r e s t rate is 8 . 7 % .
T h e c o m p o u n d i n g p e n o d is m o n t h l y , o r 12 t i m e s p e r y e a r
T h e t e r m (in y e a r s ) is 10 y e a r s .
The future value is
unknown.
T h e G I C is w o r t h $ 5 9 4 8 5 . 7 8 ,
C S B : T h e p n n e i p a l is $ 1 0 0 0 0 .
T h e a n n u a l i n t e r e s t rate is 6 . 4 % .
The
The
Ttie
The
c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r
t e r m (in y e a r s ) is 10 y e a r s ,
future value is
unknown
C S B IS w o r t h $ 1 8 5 9 5 8 6 ,
D e p o s i t i n v e s t m e n t : T h e r e g u l a r p a y m e n t a m o u n t is
$12500,
T h e p a y m e n t f r e g u e n c y is s e m i - a n n u a l , o r 2 t i m e s p e r
year.
13 6 6 1 , 7 1 -- 10 0 0 0 = 3 6 6 1 . 7 1
T h e n u m b e r o f p a y m e n t s is 2 0 ,
$ 3 6 6 1 . 7 1 i n v e s t e d f o r 1 y e a r at 6 . 2 % c o m p o u n d e d
annually g r o w s to $ 3 8 8 8 . 7 4 .
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h p a y m e n t
penod.
T h e a n n u a l i n t e r e s t rate is 4 . 9 % ,
$ 3 8 8 8 . 7 4 is l e s s t h a n $ 1 0 0 0 0 , s o C h a n d r a will n o t h a v e
e n o u g h for 4 years.
T h e c o m p o u n d i n g f r e q u e n c y is s e m i - a n n u a l , or 2 t i m e s
per year.
The future
value
is
unknown.
T h e i n v e s t m e n t is w o r t h $ 3 1 7 7 0 . 6 0 .
F o u n d a t i o n s of M a t h e m a t i c s 12 S o l u t i o n s M a n u a l
1-27
Total 59 4 8 5 J 8 + 18 595.86 + 31 770,60 = 109 8 5 2 24
P o r t f o l i o 2 is w o r t t i $ 1 0 9 8 5 2 . 2 4
P o r t f o l i o 2 is w o r t t i m o r e t t i a n p o r t f o l i o 1.
2
1 r. tiif.1 V
,
A. Y e s , t t i e y c a n i n v e s t t h e $ 6 0 0 0 n o w in a G I C t h a t
earns as high an mterest rate a s possible a n d then begin
. . q . l t .
1
1I}(1) + 50 = 60SO
. ! f>'o -s .i [H.ml
n
•X
.
4. V
4, V
h ./
V
,
0 ,
l O i . q ' so
1 '0 (X V) ~- ( 8 . 1 3 0 )
10 v
10(1(1. I 30
1.30. (/. ¥) = ( 1 0 , 1 5 0 )
K
Chapter Task, page 7 3
pix • '.(I ti'-4 del.Minine s o m e p o i n t s
n l l h . 'UlO.Uou
l o p o I no / o . ix. V) (2. 7 0 )
10.4) » no no, ( o y) ( 4 , 9 0 )
1(4Ol . SO 110
7) = (5 11 <'
i n v e s t i n g t h e i r m o n t h l y s a v i n g s in t h e s a v i n g s a c c o u n t ,
B . It will t a k e a b o u t 3 2 y e a r s . | |
4.5
= 16 years, so $ 6 0 0 0
will g r o w to 1 3 / .loQ in 1 6 y e a r s a n d t h e n $ 1 2 0 0 0 will
g r o w t o $ 2 4 0 0 0 in 3 2 y e a r s . )
10 A
V
w h i c h earns a g o o d rate of interest.
so
3
3{)()
4 so
400
They also need to save m o n e y each month to be able to
g o in 3 y e a r s .
C S i n c e $ 2 3 T-'-.n 3 n 8 4 6 = $ 1 6 4 3 4 . t h e y n e e d a
regular p a y m e n t investment with a future value of $16
4 3 4 , w h i c h will r e q u i r e a r e g u l a r p a y m e n t o f $ 4 3 1 . 0 6 .
Therefore, they need to save $431.06 each month.
D. T h e y will n e e d t o w a i t a n o t h e r 4 m o n t h s . In 4 m o r e
m o n t h s , t h e i r s a v i n g s a c c o u n t will g r o w t o $ 1 8 3 8 1 . 3 3
a n d , c o m b i n e d w i t h t h e i r G I C . w h i c h is still w o r t h $ 6 8 4 6
(it will n o t e a r n a n y i n t e r e s t o v e r t h o s e 4 m o n t h s s i n c e
t h e c o m p o u n d i n g is a n n u a l ) , t h e y will h a v e $ 2 5 2 2 7 3 3 ,
T h e y will n e e d $ 2 3 2 8 0 ( 1 , 0 8 ) = 2 5 1 4 2 . 4 0 .
yA)
h
T)0
h
«jO
t
130
SC
0
Chapter 1 Diagnostic Test, T R page 56
.
q
5 4
-.li'.O,
4 / n
gids
3i.34
Ony<
3«S<
' 1(5
654
decimal- ^
= 1,110,., or 1.11 t o t w o d e c i m a l p l a c e s
589
p e r c e n t : 1.11 • 1 0 0 = 1 1 1 %
4. a ) $ 1 0 0 0 0 • 0 . 0 6 = $ 6 0 0 b) $ 2 5 0 0 0 - 0 . 0 6 =
$1500
c) $ 5 0 0 0 0 • 0.06 = $3000
5. a | $ 1 0 OOo
1 13 - 3 1 1 2 0 0
b) $25 000
1 U
c) $50 000
I C- - $ 5 n 0 0 0
6. a ) | ; 0 . . 6
—
12
I 4 S o
/ 3
0
I
or A ;
S'41 0 0 0
. , 4 . 0 . 4 2
1,5
d ) | ; 2 . 2 5
910
A . (0, 1 0 0 ) . B . ( 3 , 2 0 0 ) . C . ( 6 . 3 0 0 ) . D. ( 9 , 4 0 0 )
7. a ) f h e p a t t e r n is t o a d d 7 1 t o g e t t h e n e x t
n u m b e r in t h e s e g u e n c e : 2 1 4 . 2 8 5 , 3 5 6 , 4 2 7 , 4 9 8 ,
569
b) Slope =
run
100
slope =
^
c) b= 1 0 0
d)
y
3y
b) T h e p a t t e r n is t o a d d half o f t h e n u m b e r t o g e t
t h e n e x t n u m b e r in t h e s e g u e n c e : 4 , 6 . 9. 1 3 . 5 ,
20.25, 30.375
c) T h e p a t t e r n is t h e d o u b l e t h e n u m b e r t o g e t t h e
mx t b
n e x t n u m b e r in t h e s e q u e n c e ; 7, 14, 2 8 , 5 6 , 1 1 2 ,
100
224
X r 100
lOOx - 3 0 0
Chapter ! t .oancial Mathematics: investing Money
1-28
4 . a , [ 2 , . O f ? ] 3 3 o , g 3 ^ ^
T o f o u r d e c i m a l p l a c e s , t h e a n s w e r is 8 . 0 1 6 9 .
. , (0.005
y
m
— 5
= 6 2 4 . 9 9 3 150
I. * 5
I
ir d e c i m a l p l a c e s , t h e a n s w e r is 6 2 4 9 9 3 2
3.2
c)
—
• 12
,
I
0 . 0 0 1 348...
T o f o u r d e c i m a l p l a c e s , t h e a n s w e r is 0 . 0 0 1 3 .
5- a) ( 3 . 4 6 ) ( 7 2 , 8 9 ) = 2 5 2 . 1 9 9 4
T o t w o d e c i m a l p l a c e s , t h e a n s w e r is $ 2 5 2 2 0 .
b) 7 . 6 9 ' = 4 5 4 , 7 5 6 . . .
T o t w o d e c i m a l p l a c e s , t h e a n s w e r is $ 4 5 4 . 7 6 ,
6. a |
c a n c h e c k t h e o t h e r n u m b e r x = ^^
Y=
7y
-300x *5600
i
- 300x f 5600
b | i) e . g . , S i n c e y = | + 1 is in t h e f o r m
-300
X ' 800
y =
+ 6, I k n e w n g h t a w a y t h a t t h e s l o p e o f t h e
f u n c t i o n is
This eguation has a slope of
^
2
c | V ) e . g . , T h e d e f i n i t i o n o f d o m a i n f o r a f u n c t i o n is t h e
s e t o f all p o s s i b l e i n p u t v a l u e s , i.e., x v a l u e s . O n a c o o r d i n a t e g r i d , t h e x - a x i s is t h e d e f i n i t i o n of t h e d o m a i n
d | II) e . g . . T h e d e f i n i t i o n o f r a n g e f o r a f u n c t i o n is t h e s e t
o f all o u t p u t v a l u e s , s o m e t i m e s c a l l e d t h e c o - d o m a i n . O n
a c o - o r d i n a t e g r i d , t h e y - a x i s is t h e r a n g e o f t h e f u n c t i o n
e | VI) e g . . T h e s e t o f i n t e g e r s is a n e x a m p l e o f d i s c r e t e '
m a t h e m a t i c s , b e i n g a set of distinct, n o n - c o n t i n u o u s
objects.
f ) iii) e . g . . T h e s e t o f real n u m b e r s is a n e x a m p l e o f
continooos mathematics, which have the property of
varying "smoothly" or continuously.
g ) vii) e . g . . T h e f u n c t i o n y = 3 x + 7 is a n e x a m p l e o f a
linear r e l a t i o n b e c a u s e it is in t h e l i n e a r r e l a t i o n f o r m y =
mx + b.
, 0 25
^
run
slope = T : 3 | 0
T h e n s e is -300 a n d t h e r u n is 7,
T h e y - i n t e r c e p t is 8 0 0 ,
b)
7y
X
3500
7y
X 4 3500
y
^ 3.3500
S l o p e . ^5?
run
slope
^
y = y+500
T h e n s e is 1 a n d t h e r u n is 7,
T h e y - i n t e r c e p t is 5 0 0 ,
1
3 . 0 ) .$110
0 1,^4
7. a) p e r i m e t e r : 2 • 6 + 2 • 2 = 16
1-4 10
b) $ 8 9 - 0 . 0 5 9 ^ t c 4 4
c) $220
Slope =
T ^
perimeter
- 1 ^ ^
16
8
—
or ^ ; 2.67; 2 6 7 %
0.0049 = $1.08
F o u n d a t i o n s of M a t h e m a t i c s 12 S o l u t i o n s M a n u a l
1-29
1 = 3;
b) p e r i m e t e r : 2 - 4 + 2 - U S = 1 6
P e f E ^ .
length
l i ^
4
or ^
y = ^^2(3) + 1
^
3
- 2.875; 287 5 %
8
c) penmet. <
•
y = ^2 + 1
%2 = 12.4
y = .^1
P 2 * l t E = l M
length
5
or ^ ;
25
2.48; 2 4 8 %
b) x - 5 y + 8 - 3 *
^ 5 y - y = 3*
length
8. a )
or 0 . 3 7 5
perimeter
4
3y = - x + 2
' 8
-^x + 2
0.375 • 100 = 3 7 . 5 %
J?^^.= A
bl
^
'.y -
penmeter
or 0 . 3 4 7 8 . . .
2
X
23
0 . 3 4 7 8 . . . • 100 = 3 4 . 7 8 %
cl J £ ^ = 2 5
perimeic^,
0.4032...
•^'^
6 % of
y = ^,
40.32%
^
a A. 5% • • 1 3 M ' O : $1000
B
, = 3:
oro.4032...
$50
I'4^1 $ 1 0 5 0 • 0 . ' .
a 7 % o f 3 i ' 0 .
3
1
y=^3
463
%,."0-0*
'i-.''
I 0.6
D. 2 . 4 % o f $ 8 0 0 : $ 8 0 0 ^ 0 . 0 2 4 = $ 1 9 . 2 0
.
T h e o r d e r from g r e a t e s t to l e a s t is C . B, A , D.
y = 1,023..
10. a | :t . 'm.iio.
». i o ^ $ 4 1 7 5
$14:>0U • $ 3 I / S
b) $ 5 1 ' . 4 9
$59
C)
y
IfdoorS
f
0.6
b) y =
+ 7
°' ^
[ 52
t) 13 - $ 9 OU
5 $ 0 <-ij - 314', Ofl
94
0
1.02
3 / 3 ».5
—
y = 344.698...
$ 1 5 0 . 9 8 + $22.65 = $173.63
y = 344.70
1 1 . a) I ; 0 . 3 3
e l f ;
0.87
15.
b ) | ; 2 . 5 8
C l f
;10.25
x = ^2y + | z ; y = ^ | x + | z ; z = 3 x + 6 y
Chapter 1 Test, T R page 64
1,a)
12. a ) T h e p a t t e m is t o s u b t r a c t 6 2 t o g e t t h e n e x t
n u m b e r in t h e s e q u e n c e : 5 8 7 . 5 2 5 . 4 6 3 . 4 0 1 , m
b) T h e p a t t e r n is t h e a d d |
277
of t h e n u m b e r to g e t t h e
n e x t n u m b e r in t h e s e q u e n c e : 1 0 . 1 2 , 1 4 , 4 . 1 7 , 2 8 ,
20 7 3 6 2 4 8 8 3 2
i t h e p a t t e r n is t o d o u b l e t h e n u m b e r t o g e t t h e n e x t
n u m b e r in t h e s e g u e n c e : 3 , 6, 1 2 . 2 4 . 4 8 , 9 6
2 0 ; U s i n g t h e r u l e of 7 2 it will t a k e 2 0
3.6
y e a r s f o r h e r i n v e s t m e n t t o d o u b l e in v a l u e .
b) T h e p n n c i p a i is $ 3 6 0 0 .
T h e a n n u a l i n t e r e s t r a t e is 3 . 6 % .
T h e c o m p o u n d i n g p e r i o d is m o n t h l y , o r 12 t i m e s
per year.
The term (in years) is unt<nown.
T h e f u t u r e v a l u e is d o u b l e $ 3 6 0 0 , o r $ 7 2 0 0 .
I used the financial application o n m y calculator:
T h e d o u b l i n g t i m e is 2 3 2 m o n t h s , o r 19 y e a r s 4
13. a ) 3 - 4 x = 3 y - 2 x
= -3-^2x + 4x
months
c) Regular payment investment: T h e regular
3y
3 - 4x ^ 2x
3y
- -2x > 3
p a y m e n t a m o u n t is $ 1 5 ,
T h e p a y m e n t f r e g u e n c y is m o n t h l y , o r 12 t i m e s p e r
--2x i_3
T t e n u m b e r o f p a y m e n t s is 2 3 2 , t h e d o u b l i n g t i m e
f o r t h e first i n v e s t m e n t .
3
T h e p a y m e n t s are m a d e at t h e e n d of e a c h
y =
^
X
3
t1
payment penod.
T h e a n n u a l i n t e r e s t r a t e is 3 . 6 % .
T h e c o m p o u n d i n g p e r i o d is m o n t h l y .
The
future
value
is
unknown.
C h a p t e r 1 . Pmancial M a t h e m a t i c s : I n v e s t i n g M o n e y
1-30
I used the financial application on mv calculator: The
i n v e s t m e n t is w o r t h $ 7 2 0 0 .
T h e r e g u l a r p a y m e n t i n v e s t m e n t is w o r t h $ 5 0 1 8 . 1 3 . T h e
s i n g l e p a y m e n t i n v e s t m e n t h a s d o u b l e d t o $ 7 2 0 0 . s o it is
worth more
2. a ) T h e p r e s e n t v a l u e is $ 4 5 0 0 .
The
annual
interest
rate is
<';'••
-'A !. !• !o
v - . l i n . .-.'6 t h e g r e a t e r
' • 3 (•'. f -f.-'ii Of. tic ' h-)V. :i,,-. ' !•(>!,nts h a v e t h e
' i'.i-- 'uii. , s . i , ' 4: f ,t,.
,|,. , : . , , , , , e n t
• H " " U ! • . . t ' l i ^ o ,,
4
unknown.
<<| 4 . 1 C
I Ir
I
per year.
t ' o - ' I'U O
111< hilt
T h e f u t u r e v a l u e is $ 6 0 0 0
I used the financial application on my calculator: He
w o u l d n e e d 9 . 6 0 7 . . . or 9 . 6 1 % a n n u a l i n t e r e s t
compounded every 2 weeks
amount
is
unknown.
T h e p a y m e n t f r e g u e n c y is e v e r y t w o w e e k s , o r 2 6 t i m e s
per year
T h e n u m b e r o f p a y m e n t s is 7 8 , 2 6 p a y m e n t s p e r y e a r f o r
3 years.
'
I „
I
HI
13'
'
j< <,
^. •III"
. . Mount to be
; , o,-'00{.
;
j
i ,',
]'.]•'
I
mik.'o-i:.
>•*• •«of'i' ' *•••
o ; < alcylator:
f •'••••^
< :' iP-'4t J ' .,' . s . ' . i 0 5 J 3 8 . . ,
R o s n v r s t c fl C i C M.^^ ,. ... : , . , , „ , ,
' 4 0 0 .38
' •
- n n u a l i n t e r e s t r a t e is 4 . 5 % .
p o u n d i n g p e r i o d is a n n u a l .
13.
I M (in y e a r s ) is 10.
'"'
"e value
is
unknown.
e financial application on my calculator:
T h e p a y m e n t s are m a d e at the e n d of e a c h p a y m e n t
period
.™.-e v a l u e of t h e s e c o n d G I C is $ 4 8 2 3 . 4 2 8 ,.
R E S P : T h e r e g u l a r p a y m e n t a m o u n t is $ 2 5 .
T h e a n n u a l i n t e r e s t rate is 9 . 6 1 % .
T h e c o m p o u n d i n g f r e q u e n c y is e v e r y t w o w e e k s , o r 2 6
times per year.
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
T h e n u m b e r o f p a y m e n t s is 2 4 0 . 12 t i m e s p e r y e a r
for 20 years.
T h e f u t u r e v a l u e is $ 6 0 0 0 ,
i used the financial application on my calculator: Trevor's
payments would need to be $ 6 6 . 5 1 ,
ii) 78
,. ^
-O .1, <4 M O p . - i r
Ot,
T h e t e r m (in y e a r s ) is 3.
payment
•.(
: n. , <i,. i,«l ,tii. r^ ...
T h e c o m p o u n d i n g p e r i o d is e v e r y t w o w e e k s , o r 2 6 t i m e s
b ) i) The regular
[...
h •
$ 6 6 51 = $ 5 1 8 7 . 8 4
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h
payment penod.
T h e a n n u a l i n t e r e s t r a t e is 3 . 8 % .
$ 6 0 0 0 - $ 5 1 8 7 . 8 4 = $812.22
T r e v o r w o u l d e a r n $ 8 1 2 . 2 2 in i n t e r e s t .
Vf/
i'
r r
T h e c o m p o u n d i n g f r e g u e n c y is m o n t h l y , o r 12
times per year.
The future
A is $ 6 0 0 0 ; P is $ 3 0 0 0 ; r i s 9 . 6 1 % o r 0 0 9 6 1
value
is
unknown.
I used the financial application on my calculator
6000 = 3000 + (3000)(0.0961)(f)
T h e f u t u r e v a l u e of t h e R E S P is $ 8 9 6 6 132
3000 = 288.3f
,
T F S A : T h e r e g u l a r p a y m e n t a m o u n t is $ 5 0 ,
It w o u l d t a k e 1 0 . 4 y e a r s , o r 10 y e a r s 2 1 w e e k s
S 3 0 0 0 to g r o w t o S 6 0 0 0
for
3. a ) 3 0 y e a r s - 12 m o n t h s = 3 6 0 p a y m e n t s
360 • $250 = $90 000
T h e p a y m e n t f r e g u e n c y is m o n t h l y , o r 12 t i m e s p e r
year.
T h e n u m b e r o f p a y m e n t s is 4 8 . 12 t i m e s p e r y e a r
for 4 years.
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h
payment penod.
b ) T h e r e g u l a r p a y m e n t a m o u n t is $ 2 5 0 .
T h e a n n u a l i n t e r e s t r a t e is 2 . 5 % .
T h e p a y m e n t f r e g u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r
T h e n u m b e r o f p a y m e n t s is 3 6 0 .
T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , o r 12
times per year.
T h e p a y m e n t s a r e m a d e at t h e e n d o f e a c h p a y m e n t
The
penod.
I used the financial application on my calculator:
The
annual
interest
rate is
unknown.
T h e c o m p o u n d i n g f r e g u e n c y is m o n t h l y , or 12 t i m e s p e r
year.
T h e f u t u r e v a l u e is $ 1 5 5 0 0 0 .
future
value
is
unknown.
T h e f u t u r e v a l u e of t h e T F S A is $ 2 5 2 1 . 3 4 3 . ..
Total value of investment portfolio on L e n s 20th
birthday:
I used the financial application on my calculator; T h e
$4823.428... + $8966.132. . + $2521 343
3 1 0 90
a v e r a g e a n n u a l interest rate w a s 3 . 3 6 % .
b) A m o u n t i n v e s t e d : G I C ; $ 2 0 0 0 ;
c ) The present
value
is
unknown.
T h e a n n u a l i n t e r e s t rate is 3 . 3 6 % ,
T h e c o m p o u n d i n g p e n o d is m o n t h l y , o r 12 t i m e s p e r
year.
= $16
R E S P ; $25 • 240 = $6000; T F S A : $50 • 48 = $2400
$2000 + $6000 + 2400 = $10 400
$10 400 was invested altogether.
T h e t e r m (in y e a r s ) is 3 0 .
T h e f u t u r e v a l u e is $ 1 5 5 0 0 0 .
I used the financial application on my calculator; Jess
w o u l d have had to deposit $ 5 6 6 6 1 . 2 1 .
F o u n d a t i o n s of M a t h e m a t i c s 12 S o l u t i o n s M a n u a l
1-31
5
b) G r e g ' s p o r t f o l i o ;
a) t ' . r i - i ' ' . j Hir 11)'In.
GIC.
I
Amount invested: GIC; $3000; CSB; $1500,
|M<>%s;iil v . j l u t ; i s 'T.'iOOO
Savings; $25 • 260 = $6500
111..- a i i i . u . i l i n l f U ' s f i-iU* i:i 'J /"•..
I h . . ( uiii|.nuitdinf) |.i.'ii«)d IS .itinuul
$3000 + $1500 + 6500
1 h i ; h-Ain
Interest e a r n e d ; $11 950.85 - $11 0 0 0 = $950 85
(tn v < M i f . } r- 4
/ / i f / u l J i / i - i/.4jH'
iiiihinw^u
$ 11 uOO
950.85
^
\ i,:....f| l i n - i i n a i K . i a l j | . p l i ( . a t i f > n (>n i n y < a l c u l a t o r ; T h e
R a t e o f return =
f i i U i n ' v a l i H - t»l t l u - ( 4 C
Rate of retum = 0 086... or 8 . 6 %
CSB:
i;, %:\A?,f
.34)
.
I h c f . H s e n t v a k » : 1 : ; $ 1 hlHJ
rti(> a n n u . i l i t i t f r < ; s l r a l e : i s
n.n':/.,
1 h.> ' •.inipoetMiiiKj p r ' i i o t l I S - i n i m , ) !
O i o o o n I .!.•/( s f ( d
I h t . tc'fir; n n v - m h 1- 3
L.Vi.sqs
i.'i" 44ii/f; t ' . - 4 i ; < - - i i n k m m n
rU)(">
I a s f n l 11,1; i i n a i K . i H i u p p i i f a l i f i i ' S i i s i y s a l c u l a t o r : T h e
l u h i i . ' vAhv
l i n ; ('.:>[{ is. $ 1 0 4 1 n 4 . i
S a v i n g s at^eoont:
! I K ; n : g u l ; i i e - j y n u m t a m o u n t is $ 2 5 .
ffif: p . i y u H ' i i ' h ' ; g u « ; n r , y r , v^«:<43-/
4n.; uo
, 0 , , , , , i u . r - i i M o i ' t s ... : ' 4 n
<<'. '^i
3125
hf.nd
,%
$4MM:
i j , e
$1000;
$59(4)
^ ' I C O ' M I » 'i[)()()<)
% 1 0ni3
|.4--f</.f . " u n i . : d :i 1 1 0 8 / / u
. '
4'0 = $887.20
887.20
R a t e o f return =
^
times per year.
times per year for
Rate of return = 0.080.. or 8 . 1 %
)!
• rp
.1 • m e n t s a r e m a d e a t t h e e n d o f e a c h p a y m e n t
G r e g h a s a s l i g h t l y g r e a t e r rate o f r e t u r n .
,/• I M 4
'14
Th
u a l i n t e r e s t r a t e is 2 . 5 % ,
. - r f i p o y n d i n g f r e q u e n c y is w e e k l y , o r 5 2 t i m e s p e r
year.
r e value
is
unknown.
. . . ^ , the financial application o n m y calculator
i ^-«^
f u t u r e v a l u e o f t h e s a v i n g s a c c o o n t is $ 6 9 2 1 . 9 4 9 . . .
Current value;
$3337,359... + $1691.543... + $6921.949...
= $11 950 85
Lou's portfolio;
B o n d : A = P ( 1 + rt)
P i s $1000; r i s 2.8%
A = 1000(1 + 0 . 0 2 h p i j )
C S B : T h e p r e s e n t valuu-
1,1114
$1360.
T h e annual interest o n o
/ < 3',,
T h e c o m p o u n d i n g p e r i o d is s e m i - a n n y a l .
T h e t e r m (in y e a r s ) is 3.
Tfie f o f t i r e v a l u e i s o n l r r i o w f i .
I used the financial application o n m y calculator: T h e
f u t u r e v a l u e o f t h e C S B is $ 1 1 7 8 . 0 6 8 . . .
S a v i n g s a c c o y n t : T h e r e g u l a r p a y m e n t a m o u n t is $ 1 2 5 ,
T h e p a y m e n t f r e q u e n c y is m o n t h l y , o r 12 t i m e s p e r y e a r .
T h e n u m b e r o f p a y m e n t s is 7 2 , 1 2 t i m e s p e r y e a r f o r 6
years.
T h e p a y m e n t s a r e m a d e at t h e e n d of e a c h p a y m e n t
period.
T h e a n n u a l i n t e r e s t r a t e is 2 . 1 5 % .
T h e c o m p o u n d i n g f r e g u e n c y is m o n t h l y , o r 12 t i m e s p e r
y03r
The
future
value
is
unknown.
I used the financial application o n m y calculator; T h e
f u t u r e v a l u e of t h e s a v i n g s a c c o u n t is $ 9 5 9 7 . 1 2 6 . . .
Current value;
$1112 + $1178.068... + $9597 126... = $11 887.19
Chaptof
1-32
I
Ir m a n c i a i M a t h e m a t i c s : I n v e s t i n g M o n e y