Question

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

$800 per year for 2 years at 16%.

$400 per year for 1 year at 8%.

$1,000 per year for 16 years at 0%.

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

$800 per year for 2 years at 16%.

$400 per year for 1 year at 8%.

$1,000 per year for 16 years at 0%.

Please show using the FV, PV, PMT, I/Y, N steps.

Answer 1

Ordinary Annuity formula

Future Value = (PMT/(I/Y))[(1+(I/Y))^N -1]

PMT = annuity payment

I/Y = rate of interest per year

N = number of years

a.

PMT = $800

I/Y = 16%

N = 2

Future Value = (800/0.16)[(1.16)² -1] = $1728

b.

PMT = $400

I/Y = 8%

N = 1

Future Value = (400/0.08)[(1.08)¹ -1] = $400

c.

When rate of interest in 0%, formula becomes

PMT = $1000

I/Y = 0%

N = 16

Future Value = 1000*16 = $16000

Annuity due formula

Future Value = (PMT/(I/Y))[(1+(I/Y))^N -1](1+(I/Y))

PMT = annuity payment

I/Y = rate of interest per year

N = number of years

a.

PMT = $800

I/Y = 16%

N = 2

Future Value = (800/0.16)[(1.16)² -1](1.16) = $2004.48

b.

PMT = $400

I/Y = 8%

N = 1

Future Value = (400/0.08)[(1.08)¹ -1](1.08) = $432

c.

When rate of interest in 0%, formula becomes PMT*N

PMT = $1000

I/Y = 0%

N = 16

Future Value = 1000*16 = $16000