Question

Find the future values of these ordinary annuities. Compounding occurs once a year. Round your answers to the nearest cent.

$900 per year for 16 years at 16%.

$450 per year for 8 years at 8%.

$400 per year for 6 years at 0%.

Rework previous parts assuming that they are annuities due. Round your answers to the nearest cent.

$900 per year for 16 years at 16%.

$450 per year for 8 years at 8%.

$400 per year for 6 years at 0%.

Answer 1

Ordinary annuity

1]

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

where P = periodic payment. This is $900

r = periodic rate of interest. This is 16%

n = number of periods. This is 16

Future value of annuity = $900 * [(1 + 16%))¹⁶ - 1] / 16%

Future value of annuity = $54,832.52

2]

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

where P = periodic payment. This is $450

r = periodic rate of interest. This is 8%

n = number of periods. This is 8

Future value of annuity = $450 * [(1 + 8%))⁸ - 1] / 8%

Future value of annuity = $4,786.48

3]

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

where P = periodic payment. This is $400

r = periodic rate of interest. This is 0%

n = number of periods. This is 6

Future value of annuity = $400 * [(1 + 0%))⁶ - 1] / 0%

Future value of annuity = $2,400

Annuity due

1]

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

where P = periodic payment. This is $900

r = periodic rate of interest. This is 16%

n = number of periods. This is 16

Future value of annuity = $900 * [(1 + 16%))¹⁶ - 1] * (1 + 16%) / 16%

Future value of annuity = $63,605.73

2]

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

where P = periodic payment. This is $450

r = periodic rate of interest. This is 8%

n = number of periods. This is 8

Future value of annuity = $450 * [(1 + 8%))⁸ - 1] * (1 + 8%) / 8%

Future value of annuity = $5,169.40

3]

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

where P = periodic payment. This is $400

r = periodic rate of interest. This is 0%

n = number of periods. This is 6

Future value of annuity = $400 * [(1 + 0%))⁶ - 1] * (1 + 0%) / 0%

Future value of annuity = $2,400