9514 1404 393
Answer:
$3891.10
Step-by-step explanation:
This question is a bit unusual in that the interest is compounded annually, but payments and withdrawals are made monthly. The effective monthly rate is ...
1.05^(1/12) -1 = 0.407412378% = i
We assume that payments to the annuity are made at the end of the month, and that withdrawals are made at the beginning of the month. (The last payment and the first withdrawal are made on the same day.)
The amount of money required in the fund is ...
A = $4000(1 -(1.00407^-360))/(1 -1.00407^-1) = $757,712.88
The amount of money needed each month to be put into the fund is P, where ...
$757,712.88 = P(1 -1.00407)^(-12(60-28))/(1 -1.00407^-1) = 194.7297P
P = $757,712.88/194.7297 = $3891.10
Yejin needs to save $3891.10 each month to meet her retirement goal.
_____
<em>Sanity check</em>
Yejin wants payments for 30 years from the fund to which she has contributed for 32 years. The similarity of the time periods means that Yejin's monthly contribution will need to be very similar to the amount she plans to withdraw.
The only ways to reduce the required contribution are to earn a higher interest on deposits, or to adjust the relative time periods (retire later).
