# Review 1 Solution

```FE Practice Problems w/ Solutions
4-114 1
If you borrow \$3,000 at 6% simple interest per year for seven years, how much will you
have to repay at the end of seven years? [4.4]
(a) \$3,000
(b) \$4,511
(c) \$1,260
(d) \$1,511
(e) \$4,260
Solution:
I = (P)(N )(i ) = (3, 000)(7)(0.06) = \$1, 260
F = P + I = 3, 000 + 1, 260 = \$4, 260
Select (e)
4-115
When you were born, your grandfather established a trust fund for you in the Cayman
islands. The account has been earning interest at the rate of 10% per year. If this account
will be worth \$100,000 on your 25th birthday, how much did your grandfather deposit on
the day you were born? [4.8]
(a) \$4,000
(b) \$9,230
(c) \$10,000
(d) \$10,150
(e) \$10,740
Solution:
(
)
P = 100,000 P ,10%, 25 = 100,000 (0.0923)= \$9, 230
F
Select (b)
4-116
Every year you deposit \$2,000 into an account that earns 2% interest per year. What will
be the balance of your account immediately after the 30th deposit? [4.9]
(a) \$44,793
(b) \$60,000
(c) \$77,385
(d) \$81,136
(e) \$82,759
Solution:
(
)
F = 2,000 F , 2%,30 = 2,000 (40.5681)= \$81,136
A
Select (d)
1
Problems choosen from Engineering Economy, 13th Edition, Sullivan, W.G., et.al., Prentice-Hall, 2006
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FE Practice Problems w/ Solutions
4-117
Your monthly mortage payment (principal plus interest) is \$1,500. if you have a 30-year
loan with a fixed interest rate of 6% compounded monthly, how much did you borrow
from the bank to purchase your house? Select the closest answer. [4.17]
(a) \$154,000 (b) \$180,000 (c) \$250,000 (d) \$300,000 (e) \$540,000
Solution:
i
= 6% = 1 2 % per month (0.5%)
mo
12
N = 30 &acute; 12 = 360 months
&eacute; (1.005)360 - 1 &ugrave;
&uacute;= 1,500 [166.7916]
P
P = 1,500
, 0.5%,360 = 1,500 &ecirc;&ecirc;
360 &uacute;
A
&ecirc;&euml;(0.005)(1.005) &uacute;
&ucirc;
P = \$250,187 per month
(
)
Select (c)
4-118
Condider the following sequence of year-end cash flows:
EOY
Cash Flow
1
\$8,000
2
\$15,000
3
\$22,000
4
\$29,000
5
\$36,000
What is the uniform annual equivalent if the interest rate is 12% per year? [4.13]
(a) \$20,422
(b) \$17,511
(c) \$23,204
(d) \$22,000
(e) \$12,422
Solution:
A = 8, 000
G = 7, 000
(
)
ATotal = 8, 000 + 7, 000 A ,12%,5
G
1.7746
ATotal = \$20, 422
Select (a)
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FE Practice Problems w/ Solutions
4-119
A cash flow at time zero (now) of \$9,982 is equivalent to another cash flow that is an
end-of-year annuity of \$2,500 over five years. Each of these two cash flows series is
equivalent to a third series, which is a uniform gradient series. What is the value of G for
this third series over the same five year time interval? [4.13]
(a) \$994
(b) \$1,150
(c) \$1,250
(d) \$1,354
(e) not enough information
Solution:
(
)
9,982 = 2,500 P , i ',5
A
P , i ',5 = 9,982 = 3.9928
A
2,500
i ' = 8% per year
(
)
(
)
9,982 = G P ,8%,5
G
7.372
9,982
G=
= \$1,354
7.372
Select (d)
4-120
What is the monthly payment on a loan of \$30,000 for seven years at a nominal interest
rate of 9% compounded monthly? [4.17]
(a) \$4,416
(b) \$258
(c) \$483
(d) \$2,700
(e) \$225
Solution:
i
= 9% = 3 % per month
mo
12
4
N = 7 &acute; 12 = 84 months
&eacute;(0.0075)(1.0075)84 &ugrave;
&uacute;= 30, 000 [0.0161]
3
A
A = 30, 000
, %,84 = 30, 000 &ecirc;&ecirc;
&uacute;
84
P 4
&ecirc;&euml; (1.0075) - 1 &uacute;
&ucirc;
A = \$483 per month
(
)
Select (c)
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FE Practice Problems w/ Solutions
4-121
A bank advertises mortgages at 12% compounded continuously. What is the effective
annual interest? [4.18]
(a) 12.36%
(b) 12.55%
(c) 12.75%
(d) 12.68%
(e) 12.00%
Solution:
r = 12%
i = er - 1 = e0.12 - 1 = 0.1275 or 12.75% compounded annually
Select (c)
4-122
If you borrow \$5,000 to buy a car at 12% compounded monthly, to be repaid over the
next four years, what is your monthly payment? [4.17]
(a) \$131
(b) \$137
(c) \$1,646
(d) \$\$81
(e) \$104
Solution:
i
= 12% = 1% per month
mo
12
N = 4 &acute; 12 = 48 months
(
)
A = 5, 000 A ,1%, 48 = 5, 000 (0.0263)
P
A = \$131.50 per month
Select (a)
4-123
If you invest \$7,000 at 12% compounded continuously, h ow much would it be worth in
three years? [4.18]
(a) \$9,449
(b) \$4,883
(c) \$10,033
(d) \$9,834
(e) \$2,520
Solution:
(
)
,12%,3 = 7, 0000e( )( )
P
= 7, 000e0.36 = 7, 000 (1.4333) = \$10, 033
F = 7, 000 F
0.12 3
Select (c)
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```