Question

eBook Find the future values of the following ordinary annuities: FV of $300 paid each 6 months for 5 years at a nominal rate of 7% compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent. $   FV of $150 paid each 3 months for 5 years at a nominal rate of 7% compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent. $   These annuities receive the same amount of cash during the 5-year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a. Why does this occur?

Answer 1

a). Calculating the Future Value of annuity:-

Where, C= Periodic Payments = $300

r = Periodic Interest rate = 7%/2 = 3.5%

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

Future Value = $3519.42

b). calculating the Future Value of annuity:-

Where, C= Periodic Payments = $150

r = Periodic Interest rate = 7%/4 = 1.75%

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

Future Value = $3555.24

c). Annuity in part(b) earnes $35.82 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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