Question

How much should be deposited each year into a retirement account starting now and continuing through year 9, if you want to be able to withdraw $59,000 per year forever, at the beginning 30 years from now? 9% per year. Enter the positive value.

Answer 1

Sol:

Withdrawal amount after 9 years = $59,000

Interest rate (r) = 9% per year

Period (n)

Funds needed 30 years from now (FV) = 59,000 / 9% = $655,555.555556

Let the annual deposits till 10 years be P (Zero years till 9 years)

FV = (P * (1 + r)^n -1/r) / (1 + r)^n

655,555.555556 = (P * (1 + 9%)^10 -1 / 9%) / (1 + 9%)^20

655,555.555556 = (P * (1.09)^10 -1/0.09) / (1.09)^20

655,555.555556 = (P * 15.1929) / 5.6044

P = 655,555.555556 / 85.1474 = $7,699.07 approx

Therefore approximate annual amount to be deposited each year into a retirement account will be $7,699.07