Question

8. Problem 5.19 Click here to read the eBook: Future Value of an Ordinary Annuity Click here to read the eBook: Finding Annuity Payments, Periods, and Interest Rates Problem Walk-Through FUTURE VALUE OF AN ANNUITY Your client is 33 years old. She wants to begin saving for retirement, with the first payment to come one year from now. She can save $2,000 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. 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: $

Answer 1

Current Age = 33 years, Return from stock market = 7%, Annual saving = $ 2000

Answer a - How much she will have at the age of 65 - ?

We will have to use financial calculator to solve this

Assuming she is investing $ 2000 stock every year starting one year from now, so we will have to calculate future value

PMT ( Annual saving) = $ 2000
I/Y ( Return ) = 7%
N ( No of contribution till she reached age 65) = 65-33 = 32
Amount she will have at age of 65 i.e. future value = ?

PMT = 2000, I/Y = 7, N = 32, FV = ? ( Please insert in financial calculator )
FV = $ 220436.31

She will have $ 220,436.31 at the age of 65

Answer b - How much she will have at the age of 70
we will have to repeat same steps which we used for solving question a

PMT = $ 2000 ( Annual saving)
i/y = 7% ( Annual rate of return )
N = 70-33 = 37 ( No of saving or no of years left for reaching 70)
Amount she will have at age of 70 i.e. FV = ?

PMT = $2000, I/Y= 7, N = 37, FV=?

FV = $ 320,674.80

She will have $ 320,674.80 at the age of 70.

Answer c - We have to calculate how much she will able withdraw annually every year for 20 years if she retires at age of 65 or 70

Part 1 - How much she will be able to withdraw every year 20 years after retire at 65

Ans - Assuming first withdrawals start at age of 66 and withdrawal is made at end of every year then

No of withdrawals = 20 ( 20 years)
I/Y = 7 (annual rate of return)
PV = $ 220436.31 ( Amount she will have at age of 65 )
PMT = ? ( How much year withdrawal she can make)

N = 20, I/Y = 7, PV = 220436.31, PMT = ?
PMT = $ 20807.63

She will be able to withdraw every year $ 20,807.63 every year till 20 years if she retires at age of 65

Part 2 - How much she will be able to withdraw every year 20 years after retire at 70

Ans - Assuming first withdrawals start at age of 71 and withdrawal is made at end of every year then

No of withdrawals = 20 ( 20 years)
I/Y = 7 (annual rate of return)
PV = $ 320674.80 ( Amount she will have at age of 70 )
PMT = ? ( How much year withdrawal she can make)

N = 20, I/Y = 7, PV = 320674.80, PMT = ?
PMT = $ 30,269.43

She will be able to withdraw every year $ 30,269.43 every year till 20 years if she retires at age of 70