Question

Assume a problem statement involves only single amounts, that is, no series or gradients, and the interest rate is stated as 12% per year compounded quarterly. For the following n values, determine the proper interest rate to use in the factor equations: (a) n 20 quarters; (b) n 10 semiannual periods; (c) n 5 years

Answer 1

Ans. Nominal annual rate, i = 12%

Effective quarterly interest rate, q = 12/4 = 3%

Annual effective interest rate, a = (1+0.03)^4 - 1 = 0.12551 or 12.551%

a) When n = 20 quarters, then the effective quarterly interest rate of 3% should be used.

c) When n = 10 semiannual coupons, then effective semiannual rate must be used,

Semiannual interest rate, s = (1+a)^0.5 - 1 =  (1+0.12551)^1/2 - 1 = 0.0609 or 6.09%

d) When n = 5 years, then the effective annual interest rate of 12.551% should be used.

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