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.**

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