Answers to Problem Set 4
1.
(a) i
6
= 0.12/6 = 0.02 or 2% per two months.
Note that the nominal rate per two months is also given by r
6
= 0.12/6
= .02. In general, it
is always the case that
The effective rate per compounding period
=
The nominal rate per compounding period
Or simply i
m
= r
m
, where m is the compounding frequency.
The nominal
rate per 4 months (i.e., 1/3 of a year) is
r
3
= r
1
/3=.12/3 =
0.04
(b) r/6 months = 0.02*3 = 6%
(c) r/2 yrs = 0.02*12 = 24%
2.
i = (1 + 0.04)
4
– 1 =
.1699 or 16.99%
3.
Here we have to take a single amount (5000) and take it 8 years back which is the same as
2 x 8 = 16 sixmonth periods. Therefore we need the effective semiannual rate i
2
. Since the
compounding period is six months (i.e., the compounding frequency is 2 times a year), we
can simply divide the nominal annual rate by the compounding frequency to get,
I
2
= .08/2 = 0.04
Therefore the value of the amount in terms of year “8” dollars is
P = 5000(P/F,4%,16) = 5000(0.5339) = $2669.50
Another way to this is to find
the effective annual rate i
1
= (1+i
2
)
2
1 and then bring the
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 Winter '11
 Panzer
 6 months, 2%, compounding period, 1.85%

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