Question

How much will you have to save each month until retirement if you want to retire in 35 years and withdraw $350,000 per year for 25 years during retirement and expect to earn 11% until retirement and 6% during retirement?

A. $4,685

B. $908

C. $2,135

D. $719

Answer 1

Note: It is assumed that Interest DURING retirement is ANNUALLY COMPOUNDED & UNTIL retirement is MONTHLY COUMPOUNDED.

PV of Annuity = P*[1-{(1+i)^-n}]/i

Where, P = Annuity = 350000, i = Interest Rate = 0.06, n = Number of Periods = 25

PV at retirement = 350000*[1-{(1+0.06)^-25}]/0.06 = 350000*0.767/0.06 = $4474174.66

FV of Annuity = P*[{(1+i)^n}-1]/i

Where, FV = 4474174.66, i = Interest Rate = 0.11/12 = 0.009167, n = Number of Periods = 35*12 = 420

Therefore,

4474174.66 = P*[{(1+0.009167)^420}-1]/0.009167

41013.27 = P*45.17605

Therefore, Amount to be deposited each month = P = 41013.27/45.17605 = $907.85 which is equivalent to $908

Therefore, (B) $908