Question

Assume that you contribute $250 per month to a retirement plan for 25 years. Then you are able to increase the contribution to $500 per month for another 25 years. Given a 9.0 percent interest rate, what is the value of your retirement plan after the 50 years?

Answer 1

The retirement plan sees contributions of $ 250 per month for 25 years, followed by monthly contributions of $ 500 for another 25 years (300 months). Annual Interest Rate = 9 %

Monthly Interest Rate = (9/12) = 0.75 % per month

Assuming that contributions are made at the beginning of each month, the total future value of these monthly deposits would be equal to the retirement plan value after 25 years.

Deposit 1 Future Value = D1 = {250 x (1.0075)^(300) + 250 x (1.0075)^(299) + ....+ 250 x (1.0075)^(1)} x (1.0075)^(300) = $ 2656772.44 ~ $ 2656772

Deposit 2 Future Value = D2 = 500 x (1.0075)^(300) + 500 x (1.0075)^(299) + 500 x (1.0075)^(298) + ....+ 500 x (1.0075) = $ 564765.18 ~ $ 564765

Total Value of Retirement Plan = D1 + D2 = 2656772 + 564765 = $ 3221538

NOTE: If Deposits are assumed to be made at the end of each month then

- D1 = {250 x (1.0075)^(299) + 250 x (1.0075)^(298) + ............+ 250} x (1.0075)^(300) = $ 2636995

- D2 = 500 x (1.0075)^(299) + 250 x (1.0075)^(298) + ....+ 500 = $ 560561

Total Retirement Plan Value = 2636995 + 560561 = $ 3197556