Question

9-15 Find the future values of the following ordinary annuities:

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

b. FV 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 annuity in part (b) earns $101.75 more than the one in part (a) over the five years. Why does this occur?

Answer 1

a). calculating the Future Value of annuity:-

Where, C= Periodic Payments = $400

r = Periodic Interest rate = 12%/2 = 6%

n= no of periods = 5 years*2 = 10

Future Value = $5272.32

b). calculating the Future Value of annuity:-

Where, C= Periodic Payments = $200

r = Periodic Interest rate = 12%/4 = 3%

n= no of periods = 5 years*4 = 20

Future Value = $5374.07

c). Annuity in part(b) earnes $101.75 more than part(a) because in part(b) the payment and Interest compounding frequency is higher which is 4 per year while in part(a) it is only 2 per year. In compounding, Interest on Interest is earned and when the compounding frequency in a period is higher it earns more Interest. Thus, part(b) earns higher than part(a).

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