Question

9-16 Find the present values of the following ordinary annuities:

a. PV of $400 each six months for five years at a simple rate of 12 percent, compounded semiannually

b. PV of $200 each three months for five years at a simple rate of 12 percent, compounded quarterly

c. The annuities described in parts (a) and (b) have the same amount of money paid into them during the five-year period and both earn interest at the same simple rate, yet the present value of the annuity in part (b) is $31.46 greater than the one in part (a). Why does this occur?

Answer 1

We can calculate the desired result in excel sheet as follows:

Formulas used in the excel sheet are:

A) Present Value of Ordinary Annuity = $ 2,944.03

B) Present Value of Ordinary Annuity = $ 2,975.49

C) The present value of the annuity in part (b) is $31.46 greater than the one in part (a) because the effective rate that is earned when the amount is compounded quarterly is greater than semi annual compounding due to which there is difference in the present values.

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