April 2015
HW#2 ‫ طارق البحري‬.‫د‬
1. What is the present equivalent value of the following future receipts?
a. $1,000, 5 years from now at 14% compounded semiannually. Answer: $508.
b. $9,000, 10 years from now at 8% compounded quarterly.
c. $25,000, 8 years from now at 9% compounded monthly.
d. $105,000, 12 years from now at 13% compounded weekly.
0
1
a)
14%
2
b)
8%
4
.‫اإلحسان يَ ُحطُ من قدر من يتَلَّقونه‬
‫‪April 2015‬‬
‫د‪ .‬طارق البحري ‪HW#2‬‬
‫)‪c‬‬
‫‪9%‬‬
‫‪12‬‬
‫)‪d‬‬
‫‪13%‬‬
‫‪52‬‬
‫الحب جنون مؤقت عالجه الزواج‪.‬‬
April 2015
HW#2 ‫ طارق البحري‬.‫د‬
2. What single equivalent amount will accumulate from each of the following
investments?
a. $1,500 in 5 years at 12% compounded semiannually. Answer: $2,686.
b. $5,000 in 9 years at 16% compounded quarterly.
c. $1,500 in 13 years at 6% compounded monthly.
d. $4,500 in 15 years at 13% compounded daily.
0
1
2
a)
3
12%
2

b)
16%
4
‫ إذا أردت أن يحبك‬:‫خالصة الكالم‬
.‫ ازهد فيما بين أيديهم‬،‫الناس‬
‫‪April 2015‬‬
‫د‪ .‬طارق البحري ‪HW#2‬‬
‫)‪c‬‬
‫‪4‬‬
‫‪6%‬‬
‫‪12‬‬
‫‪‬‬
‫)‪d‬‬
‫‪13%‬‬
‫‪365‬‬
‫الرجل يستطيع أن يكون سعيداً‬
‫ما دام ال يحب زوجته‪.‬‬
April 2015
HW#2 ‫ طارق البحري‬.‫د‬
3. What series of equal payments are equivalent to the following present
amounts?
a. $13,000 in 6 years at 8% compounded quarterly with quarterly payments.
Answer: $688.
b. $20,000 in 2 years at 15% compounded monthly with monthly payments.
c. $6,000 in 4 years at 10% compounded quarterly with semiannual payments.
d. $10,000 in 50 months at 9% compounded monthly with monthly payments.
e. $1,500 in 5 years at 13% compounded annually with quarterly payments.
0
1
2
∫
∫
∫
∫
a)
8%
4
b)
15%
12
‫تستح من إعطاء القليل‬
‫ال‬
ِ
.‫فإن الحرمان أقل منه‬
‫‪April 2015‬‬
‫د‪ .‬طارق البحري ‪HW#2‬‬
‫)‪c‬‬
‫‪10%‬‬
‫‪2‬‬
‫)‪d‬‬
‫‪9%‬‬
‫‪12‬‬
‫)‪e‬‬
‫يبدو أنها تحبك حقيقة بدليل أنها‬
‫تزوجت من شخص أخر غيرك‪.‬‬
April 2015
HW#2 ‫ طارق البحري‬.‫د‬
4. What series of equal payments are equivalent to the following future amounts?
a. $8,000 in 6 years at 16% compounded semiannually when payments are
semiannual. Answer: $422.
b. $4,000 in 12 years at 6% compounded quarterly when payments are annual.
c. $25,000 in 10 years at 12% compounded monthly when payments are quarterly.
d. $15,000 in 5 years at 8% compounded semiannually when payments are annual.
e. $70,000 in 7 years at 20% compounded quarterly when payments are monthly.
1
0
2
a)
16%
2
b)
0.06
4
‫إذا لم تزد على الحياة‬
.‫شيئا فأنت زائ ٌد عليها‬
‫‪April 2015‬‬
‫د‪ .‬طارق البحري ‪HW#2‬‬
‫)‪c‬‬
‫‪12%‬‬
‫‪4‬‬
‫‪0.03‬‬
‫‪3‬‬
‫)‪d‬‬
‫‪0.08‬‬
‫‪2‬‬
‫)‪e‬‬
‫‪20%‬‬
‫‪4‬‬
‫يتكون الزوجان السعيدان من رجل يفعل ما‬
‫تريده المرأة وامرأة تفعل ما تريده هي‪.‬‬
April 2015
HW#2 ‫ طارق البحري‬.‫د‬
5. What is the present value of the following series of prospective payments?
a. $600 a month for 3 years 13% compounded annually.
b. $5,000 a year for 5 years at 16% compounded semiannually.
c. $2,000 each year for 10 years at 8% compounded quarterly.
d. $14,000 each quarter for 4 years at 12% compounded monthly.
0
2
1
a)
b)
0.16
2
‫إما نختار أن نحيا حياتنا أو نترك‬
.‫غيرنا يحياها نيابة عنا‬
‫‪April 2015‬‬
‫د‪ .‬طارق البحري ‪HW#2‬‬
‫)‪c‬‬
‫‪0.03‬‬
‫‪3‬‬
‫)‪d‬‬
‫‪12%‬‬
‫‪4‬‬
‫‪0.03‬‬
‫‪3‬‬
‫الحماة هو أحد األنواع البشرية‬
‫الذي يمكنه خلق مشكلة لكل حل‪.‬‬
April 2015
HW#2 ‫ طارق البحري‬.‫د‬
6. What is the accumulated values of each of the following series of payments?
$5,000 semiannually for 10 years at 6% compounded monthly.
12%
4
$5,000
20
0.0304
‫نسيان غاية المرء هو أكثر‬
.ً‫أشكال الغباء انتشارا‬
April 2015
HW#2 ‫ طارق البحري‬.‫د‬
7. Find the equal –annual-payment series that would be equivalent to the
following increasing series of payments if the interest rate is 12% (a)
compounded annually; (b) compounded continuously. Answer: b. $1,105.
End of year
1
2
3
4
5
6
7
1
2
Payments
$600
$800
$1,000
$1,200
$1,400
$1,600
$1,800
3
4
5
6
7
$1,800
a)
7
$600 $200
0.12
b)
7
$600 $200
0.1275
‫يتم إنجاز األعمال في موعدها‬
.‫الصحيح في المفكرة فقط‬
April 2015
HW#2 ‫ طارق البحري‬.‫د‬
8. Find the present value equivalent to the following geometrically decreasing
series of payments. A first-year base of $10,000 decreasing at 3% per year, to
year 7 at an interest rate of 9% compounded continuously. Answer: $45,879.
0
1
2
3
4
5
6
7
‫ الخطوة األولى‬،‫بُعد المسافة ال يهم‬
.‫فقط هي األكثر صعوبة‬
April 2015
HW#2 ‫ طارق البحري‬.‫د‬
9. If compounding is quarterly, what effective annual interest rate and what
nominal interest rate will make the following values of P = $1,000;
F = $3,000; n = 6 years equivalent. Answer: 20.1% per year, 18.7%
compounded quarterly
0
1
2
3
4
5
4.68%
4
14
0.187
4
‫ الخطوة األولى‬،‫بُعد المسافة ال يهم‬
.‫فقط هي األكثر صعوبة‬
April 2015
HW#2 ‫ طارق البحري‬.‫د‬
10. If compounding is monthly, find the effective monthly interest rate, the
effective annual interest rate that will make the following values of F and A
equivalent for the values n shown.
a. F = $5,000; A = $500 annual payments; n = 8 years.
b. F = $16,500; A = $299 monthly payments; n = 4 years.
0
1
3
2
15
a)
 Solving using calculator:
0.0629
12
.‫الحاجة الملحة هو نقطة بداية كل اإلنجازات‬
‫‪April 2015‬‬
‫د‪ .‬طارق البحري ‪HW#2‬‬
‫)‪b‬‬
‫‪ Solving using calculator:‬‬
‫‪12‬‬
‫‪16‬‬
‫‪0.0697‬‬
‫‪12‬‬
‫الحمد هلل أنني لم أخلق رجالً حتى‬
‫ال أتزوج امرأة (فيلسوفة)‪.‬‬
April 2015
HW#2 ‫ طارق البحري‬.‫د‬
11. A series of payments ($10,000, first year, $9,000, second year, $8,000
third year, $7,000, fourth year, and $6,000, fifth year) is equivalent to
what present amount at 10% interest compounded annually,
compounded continuously? Solve using the gradient factors and then by
using only the single-payment present-worth factors.
0
1
2
$9,000
3
$8,000
4
$7,000
5
$6,000
 Using gradient factors:
 Using present worth factors:
 Using gradient factors:
‫الرغبة الواهنة ال ينتج‬
.‫عنها إنجازات عظيمة‬
‫‪April 2015‬‬
‫د‪ .‬طارق البحري ‪HW#2‬‬
‫‪ Using present worth factors:‬‬
‫الرجال يحلمون قبل الزواج‪،‬‬
‫ويستيقظون بعده‪.‬‬
April 2015
HW#2 ‫ طارق البحري‬.‫د‬
12. A petroleum engineer estimates that the present production of 400,000
barrels of oil during this year from a group of 10 wells will decrease at
the rate of 15% per year for years 2 through 10. Oil is estimated to be
worth $25 per barrel if the interest rate is 10% compounded annually,
what is the equivalent present amount of the prospective future receipts
from the wells?
$10,000,000
ً ‫عدد البراميل مضروبا‬
‫في سعر كل برميل‬
0
1
2
10
3
:‫ الحل األول‬
0.1
:A10 ‫في حال طلب حساب قيمة‬
-0.15
10
$10,000,000
-0.15
0.2941
10
)‫ (أسهل‬:‫ حل آخر‬
-0.15
$10,000,000
0.10
-0.15
‫آبار‬
wells
prospective
‫المحتمل‬
‫الطريق إلى القمة نادرا‬
.‫ما يكون مزدحما‬
April 2015
HW#2 ‫ طارق البحري‬.‫د‬
13. A city that was planning an addition to its water supply and distribution
system contracted to supply water to a large industrial user for 10 years
under the following conditions: The first 5 years of service were to be paid
for in advance, and the last 5 years at a rate of $45,000 a year payable at the
beginning of each year. Two years after the system is in operation the city
finds itself in need of funds and desires that the company pay off the entire
contract so that the city can avoid a bond issue.
a. If the company uses 9% interest compounded annually in calculating a
fair receipt on the contract, what amount can it expect? Answer:
$147,328.
b. If the company uses 20% interest compounded annually, how much is
the difference between what the company would consider a fair value
for the contract and what the city considers to be a fair value? Answer:
$53,864
0
1
2
3
5
4
6
7
8
9
10
$45,000
a)
$45,000
b)
20
،‫الناجحون ال يفعلون أشياء مختلفة‬
.‫بل يفعلون األشياء بطريقة مختلفة‬
April 2015
HW#2 ‫ طارق البحري‬.‫د‬
14. a young couple have decided to make advance plans for financing their
3-year-old son’s college education. Money can be deposited at 7%
compounded annually. What annual deposit on each birthday from the 4 th
to the 17th inclusive must be made to provide $16,000 on each birthday
form the 18th to the 21st inclusive?
$16,000
0
1
2
3
1
5
6
7
1
1
:)
10
11
12
13
11
15
16
17 11
11
20 21
(‫) قسط عند‬11( ‫ يمكن حساب القيمة المستقبلية لعدد‬
14
inclusive
‫شامل‬
?
0.07
:)
$16,000
( ‫) أقساط مستقبلية بد ًء من‬1( ‫) كأنها ( ) لعدد‬
( ‫ يمكن اعتبار( )عند‬
4
0.07
22.55 A
(eng-hs.net)
4
‫ألي مالحظات أو شكاوي بخصوص النوتات‬
)SMS ‫أو خدمات الموقع (واتساب أو‬
)9 4444 360 ‫(إدارة التدريب‬
‫إنسان لم يرتكب أخطاء‬
.‫باألغلب لم يحاول أبدا‬
April 2015
HW#2 ‫ طارق البحري‬.‫د‬
15. A bond is offered for sale for $1,120. Its face value is $1,000 and the
interest is 11% payable annually. What yield to maturity will be received if
the bond matures 10 years hence? Find the bond’s current yield. Answer:
9.12%, 9.82%.
= $1,000
= $110
0
3
2
1
4
5
6
7
1
1
10
= $1,120
$110
1
$1,120
.‫) ونعوض فيها بالمعلوم لدينا‬bond( ‫ سنكتب معادلة الـ‬
10
$110
$1,000
10
$1,120
Solving using try and error:
‫إنه نوع من المتعة أن‬
.‫تفعل المستحيل‬
April 2015
HW#2 ‫ طارق البحري‬.‫د‬
16. To purchase a used automobile, $6,000 is borrowed immediately. The
repayment schedule requires equal monthly payments of $264.72 to be
made over the next 24 months. After the last payment is made, any
remaining balance on the loan will be paid in a single lump sum. The
effective annual rate of interest on this loan is 19.56% based on monthly
compounding. Find the nominal interest rate and the lump sum paid at the
end of the loan.
= $6,000
0
1
∫
2
∫
∫
∫
24 months
‫ = ) وكذلك قيمة األقساط المدفوعة عند نفس التاريخ‬24( ‫ سيتم حساب قيمة القرض عند‬
.‫وحساب الفرق بين القيمتين‬
24
$6,000
0.015
24 $264.72
‫إنهم يستطيعون ألنهم يعتقدون‬
.‫أنهم يستطيعون‬