Question

Future value of an annuity Using the values below, answer the questions that follow. (Click on the icon located on the top-right corner of the data table below in order to copy its contents into a spreadsheet.) Interest rate Deposit period (years) Amount of annuity $3,000 11% a. Calculate the future value of the annuity, assuming that it is (1) An ordinary annuity. (2) An annuity due. b. Compare your findings in parts a(1) and a(2). All else being identical, which type of annuity-ordinary or annuity due—is preferable as an investment? Explain why. a. (1) The future value of the ordinary annuity is $ 58,684.29. (Round to the nearest cent.) (2) The future value of the annuity due is $ 65,139.56. (Round to the nearest cent.) b. Compare your findings in parts a(1) and a(2). All else being identical, which type of annuity is preferable as an investment? (Select the best answer below.) O O Annuity due, because it yields a greater future value. Ordinary annuity, because it yields a greater future value.

Answer 1

a]

1]

Future value of annuity = P * [(1 + r)n - 1] / r,

where P = periodic payment. This is $3,000

r = periodic rate of interest. This is 11%

n = number of periods. This is 11

Future value of annuity = $3,000 * [(1 + 11%)11 - 1] / 11%

Future value of annuity = $58,684.29

2]

Future value of annuity = P * (1 + r) * [(1 + r)n - 1] / r,

where P = periodic payment. This is $3,000

r = periodic rate of interest. This is 11%

n = number of periods. This is 11

Future value of annuity = $3,000 * (1 + 11%) * [(1 + 11%)11 - 1] / 11%

Future value of annuity = $65,139.56

b]

Annuity due is preferable because it yields a higher future value