Question

Bill decides to save for retirement. The company he chooses offers 6.3% compounded annually. Bill decides to make $3,000 yearly deposits into his account for the next 30 yrs. Then for the 25 years following his final deposit, Bill plans on taking out an equal amount of money at the end of every year.

How much will Bill be able to withdraw each year for the 25 years after his last deposit?

How much interest is earned during this entire 55 year process?

Please show work!!!!

Answer 1

Let's calculate future Value of his deposits

Future value of ordinary annuity is

=3000(FVIFA 6.3% 30Y).

= 3000(83.3603) = 250081

Interest earned is 250081-3000×30 = 160081

B) his present value of withdrawals shall be equal to future value of payments

Let's withdrawal is x

X(PVIFA 6.3% 25Y) = 250081

X(12.4269)=250081

X is 20124

So he can withdraw 20124 per year

Interest earned is = 20124×25-250081 = 253019

Total interest earned in 55 years process is

253019+160081 = 413100