You want to retire in 30 years and be able to withdraw the equivalent of $90,000 per year (in today's dollars) from a retirement fund. Assume 3% inflation. You plan to be retired for 20 years. Assuming you can earn 12% on your investments BEFORE retirement and 7% on your investments DURING retirement, how much will you need to save per month in order to be able to fund this retirement

$662.18

Explanation:

first we must determine how much are $90,000 in 30 years:

FV = $90,000 x (1 + 3%)³⁰ = $218,453.62

since the inflation rate is expected to remain the same during the 20 years that you are retired, we must find the present value of your distributions using the interest rate as our discount rate:

PV = $218,453.62 x 10.594 (PV annuity factor, 7%, 20 periods) = $2,314,297.65

the future value of your contributions = $2,314,297.65

you can earn 12% interest rate and should be able to make 360 contributions

$2,314,297.65 = monthly contribution x 3,494.96413 (FV annuity factor, 1%, 360 periods)

monthly contribution = $2,314,297.65 / x 3,494.96413 = $662.18

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