6. Future value of an annuity Your client is 35 years old; and she wants to begi

Question

6. Future value of an annuity

Your client is 35 years old; and she wants to begin saving for retirement, with the first payment to come one year from now. She can save $15,000 per year; and you advise her to invest it in the stock market, which you expect to provide an average return of 9% in the future.

a. If she follows your advice, how much money will she have at 65? Round your answer to the nearest cent.

$  

b. How much will she have at 70? Round your answer to the nearest cent.

$  

c. 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 =$

Explanation / Answer

Hi,

Please find the correct answer as follows:

a) We need to apply the future value of annuity here

Future value of annuity = annual payment*((1+rate)^(no. of years)-1)/rate

=15000*((1+9%)^30-1)/9%

=$2044613.08

Hence, she would be able to save $2044613.08 by the end of 65 years

------------

b) Future value at 70 years = 15000*((1+9%)^35-1)/9%

=$3235661.32

Hence, she would save $3235661.32 at 70 years

--------------

c) Annual withdrawals if she retires at 65:

=>2044613.08 = annuity*(1-(1+9%)^(-20))/9%

=> annuity = 223980.16

Hence she would be able to withdraw $223980.16

------------

Annual withdrawals if she retires at 70:

3235661.32 = annuity*(1-(1+9%)^(-15)/9%

=> annuity = $401412.53

Hence she would be able to withdraw $401412.53

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