Question

How much must you deposit each year into your retirement account starting now and continuing through year 10 if you want to be able to withdraw $90,000 per year forever, beginning 32 years from now? Assume the account earns interest at 12% per year.

The amount to be deposited is determined to be $

Answer 1

Present Value at year 31 = Annual Cash Flow / Rate of Interest

where r is the rate of Return for compounding period = 12%

= 90,000 / 0.12

= 750,000

Present Value at years 10 = 750,000 / (1+r)^n

r = 0.12

n = 22

= 750,000 / (1+0.12)^22

= 61981.8827925

Future Value of Annuity Due =

r = 0.12

n = 10

61981.8827925 =

61981.8827925 = Periodic Payment * 19.6545832776

Periodic Payment = 61981.8827925 / 19.6545832776

Periodic Payment = 3153.56