Question

Find the future values of the following ordinary annuities: a. PV of $200 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. b. FV of $100 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 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). FV of Annuity = Annuity * [{1 - (1 + r)^-n} / r]

= $200 * [{1 - (1 + 0.07/2)^-(5*2)} / (0.07/2)]

= $200 * [0.2911 / 0.035]

= $200 * 8.3166 = $1,663.32

b). FV of Annuity = Annuity * [{1 - (1 + r)^-n} / r]

= $100 * [{1 - (1 + 0.07/4)^-(5*4)} / (0.07/4)]

= $100 * [0.2932 / 0.0175]

= $100 * 16.7529 = $1,675.29

c). 4th option is correct.

As the annuity in part (b) is compounded 4 times in a year, whereas the annuity in part (a) is compounded 2 times in a year, which results that the interest is compounded more times in part (b).