Question

(4-18) Find the future values of the following ordinary annuities.

            a. FV of $400 each 6 months for 5 years at a nominal rate of 12%, compounded

                semiannually

b. FV of $200 each 3 months for 5 years at a nominal rate of 12%, compounded quarterly

c. The annuities described in parts a and b have the same total amount of money paid

                into them during the 5-year period, and both earn interest at the same nominal rate,

                yet the annuity in part b earns $101.75 more than the one in part a over the 5 years.

                Why does this occur?

Answer 1

a)

rate = 12% / 2 = 6%

Number of periods = 5 * 2 = 10

Future value = Annuity * [(1 + r)ⁿ - 1] / r

Future value = 400 * [(1 + 0.06)¹⁰ - 1] / 0.06

Future value = 400 * 13.180795

Future value = $5,272.32

b)

rate = 12% / 4 = 3%

Number of periods = 5 * 4 = 20

Future value = Annuity * [(1 + r)ⁿ - 1] / r

Future value = 200 * [(1 + 0.03)²⁰ - 1] / 0.03

Future value = 200 * 26.87037

Future value = $5,374.07

c)

This is because the compounding frequency is more in part B. In part a rate of return is being compounded twice whereas rate of return is compounded four times in part B.