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Answers to Assignment No. 3
Chapter 4 Questions and Problems:
Answer to Q 6
You should compare the present values of the two annuities.
Discount
Present Value of
Present Value of
Rate
10year, $1000 annuity
15year, $800 annuity
a.
5%
7721.73
8303.73
b.
20%
4192.47
3740.38
When the interest rate is low, as in part (a), the longer (i.e., 15year) but smaller annuity is more valuable
because the impact of discounting on the present value of future payments is less severe. When the
interest rate is high, as in part (b), the shorter but higher annuity is more valuable. In this case, with the 20
percent interest rate, the present value of more distant payments is substantially reduced, making it better
to take the shorter but higher annuity.
Answer to Q 14
Semiannual compounding means that the 8.5 percent loan really carries interest of
4.25 percent per
half year
.
Similarly, the 8.4 percent loan has a
monthly
rate of
.7 percent.
APR
Period
m
Effective annual rate
= (1 + per period rate)
m
– 1
8.5%
6 months
2
(1.0425)
2
−
1 = .0868 = 8.68%
8.4%
1 month
12
(1.007)
12
−
1 = .0873 = 8.73%
Choose the 8.5 percent loan for its slightly lower effective rate.
Answer to Q 21
a.
PV = 100
×
annuity factor (6%, 3 periods)
= 100
×
⎣
⎡
⎦
⎤
1
.06
−
1
.06(1.06)
3
= $267.30
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View Full Documentb.
If the payment stream is deferred by an extra year, each payment will be discounted by an additional
factor of 1.06. Therefore, the present value is reduced by a factor of 1.06 to 267.30/1.06 = $252.17.
Answer to Q 26
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 Fall '09

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