Question

Your client is 22 years old. She wants to begin saving for retirement, with the first payment to come one year from now. She can save $13,000 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? 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

Answer 1

We can use the future value of annuity formula to calculate the total savings she will have at 65 age.

FV of annuity = P * {[(1+r)^n - 1]/r}

FV of annuity = future value of annuity i.e.Total savings at 65 age = ?

P = Savings per year = $13000

r = rate of return per year = 11%

n = number of years = 65 - 22 = 43 years

FV of annuity = 13000 * {[(1+0.11)^43 - 1]/0.11}

FV of annuity = 13000 * 799.07

FV of annuity = 10387851.05

Total savings at 65 = $1,03,87,851.05

Answer 2

We can use the future value of annuity formula to calculate the total savings she will have at 70 age.

FV of annuity = P * {[(1+r)^n - 1]/r}

FV of annuity = future value of annuity i.e.Total savings at 70 age = ?

P = Savings per year = $13000

r = rate of return per year = 11%

n = number of years = 70 - 22 = 48 years

FV of annuity = 13000 * {[(1+0.11)^48 - 1]/0.11}

FV of annuity = 13000 * 1352.70

FV of annuity = 17585094.54

Total savings at 70 = $1,75,85,094.54

Answer 3

We can use present value of annuity formula to calculate the annual withdrawals if she retires at 65

Present value of annuity = P*{[1 - (1+r)^-n]/r}

Present value of annuity = Future value of annuity at 65 = $1,03,87,851.05

P = Yearly withdrawals = ?

r = rate of return per year = 11%

n = no.of years she expects to live = 20

10387851.05 = P*{[1 - (1+0.11)^-20]/0.11}

10387851.05 = P*7.963328

P = 13,04,461.01

Annual withdrawals if she retires at 65 = $13,04,461.01

Answer 4

We can use present value of annuity formula to calculate the annual withdrawals if she retires at 70

Present value of annuity = P*{[1 - (1+r)^-n]/r}

Present value of annuity = Future value of annuity at 70 = $1,75,85,094.54

P = Yearly withdrawals = ?

r = rate of return per year = 11%

n = no.of years she expects to live = 15

17585094.54 = P*{[1 - (1+0.11)^-15]/0.11}

17585094.54 = P*7.19087

P = 24,45,475.38

Annual withdrawals if she retires at 70 = $24,45,475.38