Extra practice problems for bonds
Econ 353Spring, 2005
1) Use the following formula for a. and b.
PV 
FV
1 in
where PV is what you borrow today; FV is what you pay after n number of years.
Answers: (a) i 7%, (b) i 9%.
For (c)
PV 
pmt
pmt
pmt


....
2
1 i 1 i
1 in
pmt
1
1
i
n
1
1
1
i
1
1
1
i

pmt
i
1
1
1 i
n
PV $9000, pmt 2684. 80. n = 5 Then, use a financial calculator. Answer: i 
15%.
2
a.
0
|
|
6%
|
2
|
4
|
6
8
10
|
PV = ?
500
Enter the time line values into a financial calculator to obtain PV = $279.20, or use
the following formula: (m is number of periods within one year and n is number of
years. For example if semiannual compounding m = 2)




1

PV = FV 
i 

1  
m

mn
= $500 
10
1 

 1.06 
b.
0
|
|
3%
|
4
|


1
= $500 
0.12

1
2

2 ( 5)
= $500(0.5584) = $279.20.
8
|






12
16
20
|
PV = ?
500
Enter the time line values into a financial calculator to obtain PV = $276.84,
or


1
PV = $500 
0.12

1
4

c.
0
|
1%
1






4 ( 5)
1 
= $500 

 1.03 
2
= $500(0.5537) = $276.85.
12
| 
|
20
|
PV = ?
500
Enter the time line values into a financial calculator to obtain PV = $443.72,
or


1
PV = $500 
0.12

1
12

= $500 
1 

 1.01 






12(1)
12
= $500(0.8874) = $443.70.
3)
P C  C 2 
. . . .  C n  FV n
1 i 1 i
1 i 
1 i
Here FV 1000, C CR FV 0. 08 1000 80 , and i 0. 09. Use a
(financial) calculator to get P 935. 82
4) Bond S :
P S  C  FV
1 i 1 i
Bond L :
PL  C  C 2 
. . . .  C 15  FV 15
1 i 1 i
1 i
1 i
Use financial calculator. For both cases FV 1000 and C 100 . Now under
different interest rate scenarios the answers are:
i 0. 05 : P S 1047. 64, P L 1518. 97
i 0. 08 : P S 1018. 52, P L 1171. 19
i 0. 12 : P S 982. 14, P L 863. 78
b. The longer the term to maturity, the higher are the exponential powers on discount
rates.
5)
P C  C 2 
. . . .  C 4  FV 4
1 i 1 i
1 i 
1 i
FV 1000, CR 0. 09 . Hence, C 0. 09  1000 900.
a. (i)
829  90  90 2 
. . . .  90 4  1000 4
1 i 1 i
1 i 1 i
Use a financial calculator to get i 15%
(ii)
1104  90  90 2 
. . . .  90 4  1000 4
1 i 
1 i 1 i
1 i
Use a financial calculator to get i 6%.
b. If you pay 829 you are effectively earning 15%, which is better than 12% market
interest rate. Go for it!
6)
FV 1000, CR 10%. The annual coupon payment is 0. 01  1000 100 .
Note that the interest payments are semiannual. Thus there are going to be 2* n
payments where n is the remaining number of years. But as payments are
i
semiannual C 50 , and the discount interest rate is 2 where i is the annual
interest rate. Use the following formula
P Ci  C
1 2
1 2i
2

....
C
1 2i
2n

FV
1 2i
2n
7) a. Two years later n 8. Calculate its price at 6% for remaining 8 years
P  50  50 2 
. . . .  50 16  100016
1. 03 1. 03
1. 03
1. 03
P 1251. 22
b. Two years later n 8. Calculate its price at 12% for remaining 8 years
P  50  50 2 
. . . .  50 16  100016
1. 06 1. 06
1. 06
1. 06
P 894. 94