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E120 Principles of Engineering Economics
Fall 2010
Problem Set #3 Solutions
1.
a. Since 6 months is 6/24 = 1/4 of 2 years, using our rule (1 + 0.2)
1/4
= 1.0466
So the equivalent 6 month rate is 4.66%
b. Since one year is half of 2 years, (1.2)
1/2
= 1.0954
So the equivalent 1 year rate is 9.54%
c. Since 1 month is 1/24 of 2 years, using our rule (1 + 0.2)
1/24
= 1.00763
So the equivalent 1 month rate is 0.763%.
2.
Dropped.
3.
Using the formula for converting from an EAR to an APR quote
(1 + APR/k)
k
= 1.05
Solving for the APR
APR = k((1.05)
1/k
 1)
With semiannual payments k = 2, so APR = 4.939%
With monthly payments k = 12, so APR = 4.889%
4.
Using the PV of an annuity formula with N = 10 payments and C = $100 with r = 4.067%
per 6 month interval, since there is an 8% APR with monthly compounding: 8% / 12 =
0.6667% per month, or (1.006667)
6
– 1 = 4.067% per 6 months.
PV = ($100/0.04067) × (1 – 1.04067
10
) = $808.39
5.
To find out what is owed compute the PV of the remaining payments using the loan
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 Fall '08
 ILAN

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