Question

Ross has decided that he wants to build enough retirement wealth that, if invested at 7 percent per year, will provide him with $4,200 of monthly income for 30 years. To date, he has saved nothing, but he still has 20 years until he retires.

How much money does he need to contribute per month to reach his goal? First compute how much money he will need at retirement, then compute the monthly contribution to reach that goal. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

Annual interest rate = 7.00%
Monthly interest rate = 0.5833%

After retirement:

Monthly income = $4,200
Period = 30 years or 360 months

Amount needed at retirement = $4,200/1.005833 + $4,200/1.005833^2 + ... + $4,200/1.005833^359 + $4,200/1.005833^360
Amount needed at retirement = $4,200 * (1 - (1/1.005833)^360) / 0.005833
Amount needed at retirement = $4,200 * 150.31364
Amount needed at retirement = $631,317.288

Before retirement:

Period = 20 years or 240 months

Let monthly deposits be $x

$x*1.005833^239 + $x*1.005833^238 + ... + $x*1.005833 + $x = $631,317.288
$x * (1.005833^240 - 1) / 0.005833 = $631,317.288
$x * 520.90136 = $631,317.288
$x = $1,211.97

So, monthly contribution is $1,211.97