Question

A man aged 30 deposits $500 at the end of each month for 35 years into a registered retirement savings account fund paying interest at 4% 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 7% compounded annually. Calculate the amount of each withdrawal (annuity payment). A timeline may assist you in solving this calculation. (10 points)

Answer 1

Using financial calculator (END TVM mode)

End of each month deposits (PMT) = $500

Time period (N) = 35 years or 35 x12 = 420 periods of 1 month

Interest rate (I/Y) = 4% annually or 4/12 = 0.3333% per month

Present Value (PV) = 0

Future value (FV) calculated using financial calculator = $456,865.4685

Monthly, end of month deposits of $500 for 35 years will add up to $456,865.4685 at the end of 35th year.

Using financial calculator (BGN TVM mode)

Time period (N) = 120 periods of 1 month

Interest rate (I/Y) = 7% annually or 7/12 = 0.5833% per month

Future value (FV) = 0

Amount added up for 35 years i.e.$456,865.4685 will become present value (PV)

Monthly withdrawals (PMT) calculated using financial calculator = $5,273.83

Hence, amount of each monthly withdrawal is $5,273.83.