Question

In: Finance

4) Your client is 25 years old. She wants to begin saving for retirement, with the...

4)

Your client is 25 years old. She wants to begin saving for retirement, with the first payment to come one year from now. She can save $1,000 per year, and you advise her to invest it in the stock market, which you expect to provide an average return of 11% in the future.

If she follows your advice, how much money will she have at 65? Do not round intermediate calculations. Round your answer to the nearest cent.

$
How much will she have at 70? Do not round intermediate calculations. 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? Do not round intermediate calculations. Round your answers to the nearest cent.

Annual withdrawals if she retires at 65: $

Annual withdrawals if she retires at 70: $

Expert Solution

a]

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment. This is $1,000

r = periodic rate of interest. This is 11%

n = number of periods. This is 40

Future value of annuity = $1,000 * [(1 + 11%)⁴⁰ - 1] / 11%

Future value of annuity = $581,826.07

b]

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment. This is $1,000

r = periodic rate of interest. This is 11%

n = number of periods. This is 45

Future value of annuity = $1,000 * [(1 + 11%)⁴⁵ - 1] / 11%

Future value of annuity = $986,638.56

c]

Annual withdrawals if she retires at 65 :

PV of annuity = P * [1 - (1 + r)^-n] / r,

where P = periodic payment. We need to calculate this.

r = interest rate per period. This is 11%.

n = number of periods. This is 20.

$581,826.07 = P * [1 - (1 + 11%)^-20] / 11%

P = $581,826.07 * 11% / [1 - (1 + 11%)^-20]

P = $73,063.18

Annual withdrawals if she retires at 70 :

PV of annuity = P * [1 - (1 + r)^-n] / r,

where P = periodic payment. We need to calculate this.

r = interest rate per period. This is 11%.

n = number of periods. This is 15.

$986,638.56 = P * [1 - (1 + 11%)^-15] / 11%

P = $986,638.56 * 11% / [1 - (1 + 11%)^-15]

P = $137,207.13

jeff jeffy answered 1 year ago

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