FE Practice Problems w/ Solutions
5-631
Elin purchased a car for $10,000. she wrote a check for $2,000 as a down payment for
the car and financed the $8,000 balance. The annual percentage rate (APR) is 9%
compounded monthly, and the loan is to be repaid in equal monthly installments over the
next four years. Elin’s monthly car payment is most nearly which of the following? [5.5]
(a) $167
(b) $172
(c) 188
(d) $200
(e) $218
Solution:
i mo = 9% 12 = 3 4 % per month
N=4´ 12=48 months
(
)
A = 8, 000 A , 3 4 %, 48 = 8, 000 (0.0249) = $199.20
P
Select (d)
5-64
A specialized automatic machine costs $300,000 and is expected to save $111,837.50 per
year while in operation. Using a 12% interest rate, what is the discounted payback
period? [5.8]
(a) 4
(b) 5
(c) 6
(d) 7
(e) 8
Solution:
EOY
0
- 300, 000
1
2
3
4
( F ,12%,1) =
- 200,140 + 111,837.50 (P ,12%, 2)=
F
- 110,983 + 111,837.50 (P ,12%,3) =
F
- 31,377 + 111,837.50 (P ,12%, 4) =
F
- 300, 000 + 111,837.50 P
Cumulative PW (i = 12%)
- $300, 000.00
- $ 200,140.30
- $110,983.45
- $ 31,377.52
+ $ 39, 695.21> 0
\ Æ' = 4
Select (a)
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
5-65
With interest at 8% compounded annually, how much money is required today to provide
a perpetual income of $14, 316 per year? [5.3]
(a) $ 178,950 (b) $ 96,061
(c) $ 175,134 (d) $ 171,887
Solution:
(
14,316 = X A ,8%, ¥
P
14,316 = X (0.08)
X=
)
14,316
= $178,950
0.08
Select (a)
5-66
What is the internal rate of return in the following cash flow? [5.6]
Year End
Cash Flow ($)
(a) 12.95%
0
-3,345
(b) 11.95%
1
1,100
(c) 9.05%
2
1,100
(d) 10.05%
3
1,100
4
1,100
(e) 11.05%
Solution:
Find i% such that PW(i%) = 0
(
)
0 = - 3,345 + 1,100 P , i '%, 4
A
PW (10%) = 141.89 tells us that i '% > 10%
PW (12%) = - 3.97 tells us that i '% < 12% (but is close to 12%)
\ IRR = 11.95%
Select (b)
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FE Practice Problems w/ Solutions
5-67
A bond has a face value of $1,000, is redeamable in eight years, and pays interest of $100
at the end of the eight years. If the bond can be purchased for $981, what is the rate of
return if the bond is held until maturity? [5.3]
(a) 10.65%
(b) 12.65%
(c) 10.35%
(d) 11.65%
Solution:
(
)
VN = C P
(
)
, i %, N + rZ P , i %, N = 981
F
A
where N = 8; r = 10% per period (1,001000 = 10%); and C = Z = 1, 000
(
)
981 = 1, 000 P
(
, i%,8 + 0.10´ 1, 000 P , i%,8
F
A
try i = 10%; 466.50 + 533.49 = 999.99
try i = 12%; 403.90 + 496.76 = 900.66
by observation:
i % > 10 but very close to 10%
\ rate-of-return = 10.35%
)
Select (c)
5-70
A new machine was bought for $9,000 with a life of six years and no salvage value. Its
annual operating costs were as follows:
$7,000, $7,350, $7,717.499, … , $8,933.968
If the MARR = 12%, what was the annual equivalent cost of the machine? [5.5]
(a) $7,809
(b) $41,106
(c) $9,998
(d) $2,190
(e) $9,895
Solution:
i = 12%
f = 5%
7, 000 éê1- P ,12%, 6 F ,12%, 6 ù
ú
F
P
ë
û
PW(12%) = 9, 000 +
0.12 - 0.05
7000[1- (0.5066)(1.3401)]
= 9, 000 +
0.07
= 41,110.53
(
(
)(
)
)
AW(12%) = 41,110.53 A ,12%, 6 =41,110.53(0.2432)
P
= $9,998.08
Select (c)
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FE Practice Problems w/ Solutions
5-71
A bank offers a loan at a nominal interest rate of 6% per year to be paid back in five
equal annual installments. The bank also charges an application fee equal to 13.67% of
the loan amount. What is the effective interest that the bank is charging? [5.6]
(a) 11.65%
(b) 11.35%
(c) 12.65%
(d) 12.35%
Solution:
For simplicity, assume a loan amount of $1,000. The yearly payment due on this loan is
1,000 A ,6%,5 = 1,000 (0.2374)= $ 237.40
P
The application fee due is $1,000 (0.1367) = $136.70. Thus the borrower walks away
with $1,000 - $136.70 = $863.30. The effective interest rate being charged can be found
by solving the following equivalence equation for i':
863.30 = 237.40 P , i %,5
A
P , i %,5 = 863.30 = 3.6365
A
237.40
P ,12%,5 = 3.6048 and P ,10%,5 = 3.7908
A
A
using linear interlopation: i % = 11.65%
(
)
(
(
(
)
)
)
(
)
Select (a)
5-72
You want to deposit enough money in a bank account for your son’s education. You
estimate that he will need $8,000 per year for four years, starting on his 18th birthday.
Today is his first birthday. If you earn 12% interest, how much lump sum should you
deposit in the bank today to provide for his education? [5.3]
(a) $24,298
(b) $3,538
(c) $32,000
d) $3,963
Solution:
(
)(
P = 8, 000 P ,12%, 4 P ,12,16
A
F
3.0373
0.1631
= $3,963.07
)
Select (d)
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