Question

Your client is 38 years old; and she wants to begin saving for retirement, with the first payment to come one year from now. She can save $3,000 per year; and you advise her to invest it in the stock market, which you expect to provide an average return of 7% in the future. If she follows your advice, how much money will she have at 65? Round your answer to the nearest cent. $ How much will she have at 70? Round your answer to the nearest cent. $ She expects to live for 20 years if she retires at 65 and for 15 years if she retires at 70. If her investments continue to earn the same rate, how much will she be able to withdraw at the end of each year after retirement at each retirement age? Round your answers to the nearest cent. Annual withdrawals if she retires at 65 $ Annual withdrawals if she retires at 70 $

Answer 1

Calculation of Retirement amount if retire at 65:

P = Annual savings = $3,000

r = interest rate = 7%

n = 65 - 38 = 27 years

Accumulated amount at 65 = P * [(1+r)^n - 1] / r

= $3,000 * [(1+7%)^27 - 1] / 7%

= $3,000 * 5.21386763 / 0.07

= $223,451.47

Therefore, Amount available at 65 is $223,451.47

Calculation of Retirement amount if retire at 70:

P = Annual savings = $3,000

r = interest rate = 7%

n = 70 - 38 = 32 years

Accumulated amount at 70 = P * [(1+r)^n - 1] / r

= $3,000 * [(1+7%)^32 - 1] / 7%

= $3,000 * 7.7152708 / 0.07

= $330,654.462

Therefore, Amount available at 70 is $330,654.46

Calculation of Annual Withdrawals if retire at 65:

PV = Amount available at 65 = $223,451.47

n = 20 years

r = interest rate = 7%

Annual Withdrawal amount = [r*PV] / [1 - (1+r)^-n]

= [7% * $223,451.47] / [1 - (1+7%)^-20]

= $15,641.6029 / 0.741580997

= $21,092.238

Therefore, annual withdrawal amount if retire at 65 for 20 years is $21,092.24

Calculation of Annual Withdrawals if retire at 70:

PV = Amount available at 70 = $330,654.46

n = 15 years

r = interest rate = 7%

Annual Withdrawal amount = [r*PV] / [1 - (1+r)^-n]

= [7% * $330,654.46] / [1 - (1+7%)^-15]

= $23,145.812 / 0.63755398

= $36,304.0821

Therefore, annual withdrawal amount if retire at 70 for 15 years is $36,304.08