Question

Stan has made a $125.30 monthly deposit into an account that pays 1.5% interest, compounded monthly, for 35 years. He would now like to draw a monthly salary from the account. Determine the amount that Stan can withdraw each month for 20 years, if he plans on not having anything in the account at the end of the 20 year period and no future deposits are made to the account.
a.
$69,242.49
b.
$69,159.05
c.
$333.29
d.
$333.71

Answer 1

Monthly rate i = 0.015/12 = 0.00125.

1) Accumulate the monthly deposits for 35 years (n1 = 35·12 = 420):
FV = PMT * [((1+i)^{n1} − 1)/i]
= 125.30 * [((1.00125)^{420} − 1)/0.00125]
≈ 125.30 * 551.924 ≈ $69,156.08 (≈ $69,159.05).

2) Withdraw monthly for 20 years (n2 = 20·12 = 240) so the payment is
PMT = FV * [i / (1 − (1+i)^{−n2})]
≈ 69,156.08 * [0.00125 / (1 − (1.00125)^{−240})]
≈ $333.71.

Answer: d. $333.71.