Monica has decided that she wants to build enough retirement wealth that, if inv

Question

Monica has decided that she wants to build enough retirement wealth that, if invested at 10 percent per year, will provide her with $4,000 of monthly income for 20 years. To date, she has saved nothing, but she still has 25 years until she retires How much money does she need to contribute per month to reach her goal? First compute how much money she 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.)

Explanation / Answer

After retirement:

Monthly income = $4,000
Annual interest rate = 10%
Monthly interest rate = 0.833%
Period = 20 years or 240 months

Amount required at retirement = $4,000 * PVIFA(0.833%, 240)
Amount required at retirement = $4,000 * (1 - (1/1.00833)^240) / 0.00833
Amount required at retirement = $4,000 * 103.65308
Amount required at retirement = $414,612.32

Before retirement:

Amount required at retirement = $414,612.32
Monthly interest rate = 0.833%
Period = 25 years or 300 months

Monthly deposit * FVIFA(0.833%, 300) = $414,612.32
Monthly deposit * (1.00833^300 - 1) / 0.00833 = $414,612.32
Monthly deposit * 1,325.92961 = $414,612.32
Monthly deposit = $312.70

So, Monica needs to save $312.70 every month in order to achieve her goal.

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