Question

Bob, age, 35, has already accumulated $100,000 in retirement assets. He expects to retire at age 65 and live until age 90. He expects to earn 8% before retirement and 6% after retirement. If he makes no additional contributions to his account and he receives a fixed (non-increasing) monthly annuity from the account for life, what is the amount he could withdraw at the beginning of each month in retirement?

Answer 1

The amount he can withdraw has a future value at 65 years of age, that is, 30 years from now:

FV (90) = (100000(F/P, 8%, 30)) = 100000*10.062657 = $1,006,266

If withdrawl is made at the beginning, his first withdrawl is A and total withdrawls are (90 - 65)*12 -1 = 300. Find A

$1,006,266 = A + A(P/A, 6%/12, 299)

$1,006,266= A(1 + 154.9829)

This gives A = 1,006,266/155.9829

This gives A = 6451.13. This is the amount he could withdraw at the beginning of each month in retirement.