Question

# 1. Kathleen wants to retire on \$55,000 per year for 20 years. She estimates that she...

1. Kathleen wants to retire on \$55,000 per year for 20 years. She estimates that she will be able to earn interest at the APR of 9% compounded annually, throughout her lifetime. To reach her retirement goal, Kathleen will make annual contributions to her account for the next 35 years. One year after making her last contribution, she will take her first retirement check. How large must her yearly contributions be?

Annual Payment after retirement = \$55,000
Period = 20 years
Annual Interest Rate = 9%

Amount required at retirement = \$55,000 * PVIFA(9%, 20)
Amount required at retirement = \$55,000 * (1 - (1/1.09)^20) / 0.09
Amount required at retirement = \$55,000 * 9.12855
Amount required at retirement = \$502,070.25

Time to Retirement = 35 years

Annual Saving * FVIFA(9%, 35) = \$502,070.25
Annual Saving * (1.09^35 - 1) / 0.09 = \$502,070.25
Annual Saving * 215.71075 = \$502,070.25
Annual Saving = \$2,327.52

So, annual contribution of Kathleen is \$2,327.52

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