Question

Allen starts putting away $400 each month starting at the age of 25 in mutual funds earning about 7.5% per year. Beth invests the same funds but starts putting away $800 each month starting at age 33. How much money does each person have at age 60? Who ends up with more retirement money?

Answer 1

Formula: The Future Value of an ordinary annuity (FV)

FV= C× {[(1+r)^n]-1}/r

FV = Future value (The cummulative amount available in Future)
C= Periodic cash out flow.
r =effective interest rate for the period.
n = number of periods.

1. Allen
FV= 400× {[(1+0.0060449)^420]-1}/0.0060449
FV = $765,526.91

FV = Future value (The cummulative amount available in Future)
C= Periodic cash out flow = 400
r =effective interest rate for the period. = [(1.075)^(1/12)]- 1 = 0.0060449
n = number of periods = (60-25)x12 = 420

Retirement Money = $765,526.91

2. Beth
FV= 800× {[(1+0.0060449)^324]-1}/0.0060449
FV = $800,327.51

FV = Future value (The cummulative amount available in Future)
C= Periodic cash out flow = 800
r =effective interest rate for the period. = [(1.075)^(1/12)]- 1 = 0.0060449
n = number of periods = (60-33)x12 = 324

Retirement Money = $800,327.51

Beth ends up with more retirement money than Allen.