Question

Future Value of an Annuity for Various Compounding Periods

Find the future values of the following ordinary annuities.

1. FV of $800 each 6 months for 9 years at a nominal rate of 8%, compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent.

   $   

2. FV of $400 each 3 months for 9 years at a nominal rate of 8%, compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent.

   $   

3. The annuities described in parts a and b have the same amount of money paid into them during the 9-year period, and both earn interest at the same nominal rate, yet the annuity in part b earns more than the one in part a over the 9 years. Why does this occur?

Answer 1

a). Calculating the Future Value using Future Value of Ordinary annuity formula;-

Where, C= Periodic Payments = $800

r = Periodic Interest rate = 8%/2 = 4%(compounded semiannually)

n= no of periods = 9 years*2 = 18 (compounded semiannually)

Future Value = $20,516.33

b). Calculating the Future Value using Future Value of Ordinary annuity formula;-

Where, C= Periodic Payments = $400

r = Periodic Interest rate = 8%/4 = 2%(compounded Quarterly)

n= no of periods = 9 years*4 = 36 (compounded Quarterly)

Future Value = $20,797.75

c). The Future Value in part (b) is higher than that of Future value in part (a) because in part b annuity is paid 4 times a year and interest is also componded 4 times in a year. Since, higher the  compounding period higher is the Interest earned on interest. Thus, part b has earned higher interest than part a due to more compounding in a year.