Question

Find the future values of these ordinary annuities. Compounding occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent.

a. $400 per year for 12 years at 8%

b. $200 per year for 6 years at 4%.

c. $600 per year for 6 years at 0%.

d. Rework parts a, b, and c assuming they are annuities due.

-Future value of $400 per year for 12 years at 8%:

-Future value of $200 per year for 6 years at 4%:

-Future value of $600 per year for 6 years at 0%

Answer 1

a). $400 per year for 12 years at 8%

Calculating the future Value of Ordinary annuity:-

Where, C= Periodic Payments = $400

r = Periodic Interest rate = 8%

n= no of periods = 12

Future Value = $7590.85

b. $200 per year for 6 years at 4%.

Calculating the future Value of Ordinary annuity:-

Where, C= Periodic Payments = $200

r = Periodic Interest rate = 4%

n= no of periods = 6

Future Value = $1326.60

c). $600 per year for 6 years at 0%.

Future Value formula when Interest rate is 0%.

Future Value = periodic payments*no of periods

Where, C= Periodic Payments = $600

n= no of periods = 6

Future Value = $600*6

Future Value = $3600

d). Reworking parts a, b, and c assuming they are annuities due.

i). $400 per year for 12 years at 8%

Calculating the future Value of annuity Due:-

Where, C= Periodic Payments = $400

r = Periodic Interest rate = 8%

n= no of periods = 12

Future Value = $8198.12

ii). $200 per year for 6 years at 4%.

Calculating the future Value of annuity Due:-

Where, C= Periodic Payments = $200

r = Periodic Interest rate = 4%

n= no of periods = 6

Future Value = $1379.66

iii). When Interest rate is 0% Future Value will be same for ordinary annuity and annuity due.

So, Future Value = periodic payments*no of periods

Where, C= Periodic Payments = $600

n= no of periods = 6

Future Value = $600*6

Future Value = $3600