Question

Your client is 22 years old; and she wants to begin saving for retirement, with the first payment to come one year from now. She can save $4,000 per year; and you advise her to invest it in the stock market, which you expect to provide an average return of 6% 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.

Answer 1

Future value of investment can be computed as:

FV = C x FVIFA (i, n)

Where C = Cash investment per period = $ 4,000

             i = rate of interest = 6 %

            n = No. of period

a.

n = 65 – 22 = 43 years

FV = $ 4,000 x FVIFA (6%, 43)

   = $ 4,000 x 187.5076

   = $ 750,030.40

b.

n = 70 – 22 = 48 years

FV = $ 4,000 x FVIFA (6%, 48)

   = $ 4,000 x 256.5645

   = $ 1,026,258.00

c.

Periodic cash withdrawal can be computed using formula for PV of annuity as:

PV = C x PVIFA (i, n)

C = PV/PVIFA (i, n)

Where C = Cash withdrawal per period

             i = rate of interest = 6 %

            n = No. of period

If n = 20 years

C = $ 750,030.40/ PVIFA (6 %, 20)

   = $ 750,030.40/11.4699

   = $ 65,391.18911 or $ 65,391.19

If n = 15 years

C = $ 1,026,258/ PVIFA (6 %, 15)

   = $ 1,026,258/9.7122

   = $ 105,666.89319 or $ 105,666.89

She will earn $ 65,391.19 annually if retire in 65 years and $ 105,666.89 if retire in 70 years.