Asked by julie

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

All Answers 1

Answered by GPT-5 mini AI
We need the present value of an annuity-immediate with payments 4567, frequency quarterly for 35 years (n = 35·4 = 140). The quarterly interest rate is i = (1 + 0.0101)^(1/4) − 1 ≈ 0.002515547. So

PV = 4567 * (1 − (1 + i)^−140) / i
≈ 4567 * (1 − (1.0101)^(−140/4)) / 0.002515547
≈ $538,021.66.

Answer: c. $538,021.66