Question

A.) If you make quarterly payments of$331.00 into an ordinary annuity earning an annual interest rate of 5.47%, how much will be in the account after 4 years?

B.) If you make monthly payments of $464.00 into an ordinary annuity earning an annual interest rate of 7.4% compounded monthly, how much will you have in the account after 5 years? After 9 years?

C.) In 3 years Harry and Sally would like to have $26,000.00 for a down payment on a house. How much should they deposit each month into an account paying 8% compounded monthly?

Answer 1

Answer A.

Quarterly Payments = $331.00
Annual Interest Rate = 5.47%
Quarterly Interest Rate = 2.735%
Period = 4 years or 16 quarters

Accumulated Sum = $331.00*1.02735^15 + $331.00*1.02735^14 + ... + $331.00*1.02735 + $331.00
Accumulated Sum = $331.00 * (1.02735^16 - 1) / 0.02735
Accumulated Sum = $331.00 * 19.74070
Accumulated Sum = $6,534.17

Answer B.

Monthly Payment = $464.00
Annual Interest Rate = 7.40%
Monthly Interest Rate = 0.6167%

Accumulated Sum after 5 years = $464.00*1.006167^59 + $464.00*1.006167^58 + ... + $464.00*1.006167 + $464.00
Accumulated Sum after 5 years = $464.00 * (1.006167^60 - 1) / 0.006167
Accumulated Sum after 5 years = $464.00 * 72.33978
Accumulated Sum after 5 years = $33,565.66

Accumulated Sum after 9 years = $464.00*1.006167^107 + $464.00*1.006167^106 + ... + $464.00*1.006167 + $464.00
Accumulated Sum after 9 years = $464.00 * (1.006167^108 - 1) / 0.006167
Accumulated Sum after 9 years = $464.00 * 152.83426
Accumulated Sum after 9 years = $70,915.10