Beginning at age 35, Ms. Trinh invests $4000 each year into an IRA account until she retires. When she retires she plans to withdraw equal amounts each year that will deplete the account when she is 80. Find the annual amounts she will receive for each of the following retirement ages. Assume the account pays 5% compounded annually. (Round your final answers to two decimal places.)

Question

I used the formula A = P(1+r/n)^nt

I solved the equation and got the following answers. Does anyone agree with me or can you show me what I did wrong.

I used the formula A = 4000[(1+0.05)^25-1]/0.05

(a) Retires at age 60.
 $  190908.40

I used the formula A = 4000[(1+0.05)^30-1]/0.05

(b) Retires at age 65.
 $  265755.39

I used the formula A = 4000[(1+0.05)^35-1]/0.05

(c) Retires at age 70.
 $  361281.23
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Steve · Answer

You quoted the wrong formula, but used the correct one in your calculations. Those give the future value, given her payments.

But the question is, what amount will she receive to deplete the funds at age 80? So, use the formula in reverse to find the PV=0 at age 80.

The amounts change dramatically, since earlier retirement provides less money, and there are more withdrawals by age 80.