Question

You are planning for your retirement and have decided the following: you will retire in 35 years and would like to have $8,000 per month as retirement income for 30 years of retirement. You have access to an account that earns a 7% rate of return. a. How much will you need to have when you retire to be able to withdraw the desired $8,000 per month during your years of retirement? (Round your answer to the nearest cent) b. If you plan to save by making equal monthly deposits into your account from now until when you retire, how much does that deposit need to be? (Round your answer to the nearest cent)

Answer 1

Answer a.

Monthly payment = $8,000
Time period = 30 years or 360 months
Annual interest rate = 7.00%
Monthly interest rate = 0.5833%

Amount required at retirement = $8,000/1.005833 + $8,000/1.005833^2 + … + $8,000/1.005833^359 + $8,000/1.005833^360
Amount required at retirement = $8,000 * (1 - (1/1.005833)^360) / 0.005833
Amount required at retirement = $8,000 * 150.313637
Amount required at retirement = $1,202,509.10

Answer b.

Amount required at retirement = $1,202,509.10
Monthly interest rate = 0.5833%
Time period = 35 years or 420 months

Let monthly deposits be $x

$1,202,509.10 = $x/1.005833 + $x/1.005833^2 + … + $x/1.005833^419 + $x/1.005833^420
$1,202,509.10 = $x * (1 - (1/1.005833)^420) / 0.005833
$1,202,509.10 = $x * 156.536580
$x = $7,681.97

Monthly deposit = $7,681.97