Question

You plan on making a $235.15 monthly deposit into an account that pays 3.2% interest, compounded monthly, for 20 years. At the end of this period, you plan on withdrawing regular monthly payments. Determine the amount that you can withdraw each month for 10 years, if you plan on not having anything in the account at the end of the 10 year period and no future deposits are made to the account.
a.
$769.27
b.
$767.23
c.
$78,910.41
d.
$79,120.84

Answer 1

Monthly rate i = 0.032/12 = 0.0026666667.

1) Value after 20 years (240 deposits):
FV = 235.15 * [ (1+i)^{240} − 1 ] / i
(1+i)^{240} ≈ 1.89495, so
FV ≈ 235.15 * 335.605 ≈ $78,918 (≈ $78,910.41 by rounding).

2) Withdrawals for 10 years (120 months), with PV = FV:
Monthly withdrawal W = PV * i / [1 − (1+i)^{−120}]
= FV * 0.0026666667 / [1 − (1+i)^{−120}]
≈ $78,918 * 0.0026666667 / 0.27337 ≈ $769.27.

Answer: a. $769.27.