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problemset004answers

problemset004answers - Answers to Problem Set 4 1(a i6 =...

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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 six-month 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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