Question

In an effort to save money for early retirement, an environmental engineering colleague plans to deposit $1,200 per month, starting one month from now, into a fixed rate account that pays 8% per year compounded semi-annually. How much will be in the account at the end of 25 years? At the end of 25 years, the account will be $ 7.

Answer 1

Monthly deposit = $1,200

Annual interest rate = 8.00%
Semiannual interest rate = 4.00%

Effective annual rate = (1 + Semiannual interest rate)^2 - 1
Effective annual rate = (1 + 0.04)^2 - 1
Effective annual rate = 1.0816 - 1
Effective annual rate = 0.0816 or 8.16%

Monthly interest rate = (1 + Effective annual rate)^(1/12) - 1
Monthly interest rate = (1 + 0.0816)^(1/12) - 1
Monthly interest rate = 1.00656 - 1
Monthly interest rate = 0.00656 or 0.656%

Period = 25 years or 300 months

Future value = $1,200*1.00656^299 + $1,200*1.00656^298 + …. + $1,200*1.00656 + $1,200
Future value = $1,200 * (1.00656^300 - 1) / 0.00656
Future value = $1,200 * 931.4791865
Future value = $1,117,775

At the end of 25 years, the account will be $1,117,775