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 = 1/375 ≈ 0.0026666667.
Number of deposit months = 20·12 = 240, number of withdrawal months = 10·12 = 120.

Future value after deposits:
FV = 235.15 * [((1+i)^240 − 1)/i].

Monthly withdrawal W (level payment for 120 months leaving zero):
W = FV * [ i / (1 − (1+i)^(−120)) ].

Combining (i cancels) gives the simpler form
W = 235.15 * [ (1+i)^240 − 1 ] / [ 1 − (1+i)^(−120) ]
= 235.15 * [ (1+i)^{120}^2 + (1+i)^{120} ].

Evaluating with i = 1/375 yields W ≈ $769.27.

Answer: a. $769.27