Question

13. Problem 5.25 (Future Value of an Annuity) eBook Find the future values of the following ordinary annuities: a. FV of $400 paid each 6 months for 5 years at a nominal rate of 15% compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent. b. FV of $200 paid each 3 months for 5 years at a nominal rate of 15% compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent. C. 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? -Select-

Answer 1

a)

Future value Px[(1+r)^n-1]=r Here, 15% A Interest rate per annum B Number of years C Number of payments per per annum A:C Interest rate per period (r) BxC Number of periods (n) Payment per period (P) 7.5% 10 400 $ Future value $ 5,658.83 400/((1+7.5%)^10-1):7.5%

b)

Future value Px[(1+r)^n-1]=r Here, 15% 4 A Interest rate per annum B Number of years C Number of payments per per annum A:C Interest rate per period (r) BxC Number of periods (n) Payment per period (P) 3.75% 20 200 Future value $ 5,803.48 200x((1+3.75%)^20-1):3.75% c) The annuity in part (b) is compounded more frequently; therefore, more interest is earned on previously-earned interest.

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