Question

You plan to retire as soon as you turn 65. Upon retirement you want to receive $70,000 per year at the start of each year (first payment on day you turn 65) for the next 20 years. You are 25 years old today. You want to start saving today.

1. How much do you have to save each year (annual periods) to ensure that you will have sufficient funds to receive $70,000 per year from the age of 65? Initially, while saving, you can earn a rate of return of 10% per year compounded annually. However, once you stop saving and start spending (age 65) you can only earn a rate of return of 5% per year compounded annually on whatever savings you have accumulated.

2. Unfortunately to earn returns of 10% per year involves taking risks in the stock market. The annual standard deviation (risk) of stock market returns is 10%. How much do you need to save each year in order to be 95% confident that you will be able to receive at least $70,000 per year in retirement? Does your answer make sense relative to part 1? Why/Why not?

3. You decide that while young you are happy to invest in the stock market, but as you get older you wish to take fewer risks, and earn lower returns on your savings. For the first 15 years you expect to earn 10% per year with a standard deviation of 10%. For years 16 – 30 you expect to earn 8% per year with a standard deviation of 5%. Finally, for the last 10 years you expect to earn 5% per year with a standard deviation of 2%. How much do you need to save each year in order to be 95% confident that you will be able to receive at least $70,000 per year in retirement? Does your answer make sense relative to parts 1 and 2? Why/Why not?

Answer #1

1 | Annuity at the beginning of each year | $70,000 | |||||||||||

Number of years of annuity | 20 | ||||||||||||

Rate of return | 5% | ||||||||||||

Amount required on retirement | $915,972.46 | (Using excel PV function with Rate=5%, Nper=20,Pmt=-70000, Type=1(beginning ofperiod)) | |||||||||||

Number of years of savings | 40 | (65-25) | |||||||||||

Rate of Return | 10% | ||||||||||||

Amount of saving required per year(at beginning of each year) | $2,069.56 | (Using excel PMT function with Rate=10%, Nper=40,FV=-915972.46, Type=1(beginning ofperiod)) | |||||||||||

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