Question

5.         Suppose you start saving $15,000 per year (starting next year) for the 40 years you are working. How much can you withdraw each year for the 38 years you are retired? Assume that you earn an 8% return for the years you are saving and a 4% return for the years you are retired.

Answer 1

Step 1
Using future value of annuity formula , we can calculate the future value of yearly savings at the end of 40th year
Future value of annuity = P x {[(1+r)^n -1]/r}
Future value of annuity = value of yearly savings at the end of 40th year = ?
P = Yearly savings = $15000
r = rate of return per year for working years = 8%
n = number of working years = 40
Future value of annuity = 15000 x {[(1+0.08)^40 -1]/0.08}
Future value of annuity = 15000 x 259.0565
Future value of annuity = 3885847.78
Value of yearly savings at the end of 40th year = $38,85,847.78
Step 2
Using present value of annuity formula , we can calculate the yearly withdrawal for 38 years.
Present Value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = value of yearly savings at the end of 40th year = $38,85,847.78
P = Yearly withdrawal = ?
r = rate of return per year for retired years = 4%
n = number of retired years = 38
3885847.78 = P x {[1 - (1+0.04)^-38]/0.04}
3885847.78 = P x 19.36786
P = 200633.78
You can withdraw $2,00,633.78 each year for the 38 years you are retired.