Question

A man aged 30 deposits $600 at the end of each month for 35 years into a registered retirement savings account fund paying interest at 3% compounded annually.

Starting on his 65th birthday, he makes 120 equal monthly withdrawals from the fund at the beginning of each month. During this period, the fund pays interest at 6% compounded annually. Calculate the amount of each withdrawal (annuity payment). A timeline may assist you in solving this calculation.

Answer 1

First, let's find the future value of the monthly deposits as of age 65

n = 35 * 12 = 420 monthly deposits

PMT = 600

Effective monthly rate, r = (1 + 0.03)^(1/12) - 1

r = 0.002466269772

Now, with as the PV, let's find the monthly withdrawals for 120 months

n = 120

PV = 441,280.7896183386

Effective monthly rate, r = (1 + 0.06)^(1/12) - 1

r = 0.004867550565

The amount of each withdrawal is $4,840.4135702245