Question

Seth has a bank account which pays 1.01% interest, compounded quarterly. Seth withdraws $4,567 from the account every quarter for 35 years. Assuming that Seth does not make any deposits into this account and that the withdrawals occur at the end of every quarter, find the initial value of the account, rounded to the nearest cent.
a.
$765,824.68
b.
$767,758.39
c.
$538,021.66
d.
$539,380.16

Answer 1

Let i = 0.0101/4 = 0.002525 (quarterly rate) and n = 35·4 = 140 quarters. The present value of an ordinary annuity is

PV = 4567 * (1 - (1 + i)^(-n)) / i
= 4567 * (1 - (1.002525)^(-140)) / 0.002525
≈ $537,761.14.

The closest choice is (c) $538,021.66.