Gail Kelley deposits $300 in an account at the beginning of each 3-month period for 12 years. If the account pays interest at the annual rate of 8%, compounded quarterly, how much will she have in her account after 12 years? Round your answer to the nearest cent.
A)$15,910.28
B)$65,443.18
C)$24,282.18
D)$34,899.77
E)$48,365.45

Question

Quizplus · Accepted Answer

We can use the formula for the future value of an annuity with compounding:

$FV = PMT \cdot \frac{(1 + r/n)^{nt} - 1}{r/n}$

where PMT is the periodic payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, PMT = 300, r = 0.08, n = 4 (quarterly compounding), and t = 12 (since Gail is making payments for 12 years). Plugging in these values, we get:

$FV = 300 \cdot \frac{(1 + 0.08/4)^{4 \cdot 12} - 1}{0.08/4} \approx 24,282.18$

Therefore, Gail will have approximately $24,282.18 in her account after 12 years.

Gail Kelley Deposits $300 in an Account at the Beginning