Gail Kelley deposits $600 in an account at the beginning of each 3-month period for 8 years. If the account pays interest at the annual rate of 7%, compounded quarterly, how much will she have in her account after 8 years? Round your answer to the nearest cent.
A) $18,016.48
B) $57,281.19
C) $25,892.65
D) $34,941.44
E) $45,337.43

Question

Gail Kelley deposits $600 in an account at the beginning of each 3-month period for 8 years. If the account pays interest at the annual rate of 7%, compounded quarterly, how much will she have in her account after 8 years? Round your answer to the nearest cent. ​
A) $18,016.48
B) $57,281.19
C) $25,892.65
D) $34,941.44
E) $45,337.43

Quizplus · Accepted Answer

Gail Kelley is making a series of equal deposits at the beginning of each quarter for 8 years, which amounts to 8 * 4 = 32 periods. Since the deposits are made at the beginning of each period, this is an annuity due. The future value of an annuity due can be calculated using the formula: $FV_{\text{annuity due}} = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \times (1 + r)$, where $P$ is the payment amount per period, $r$ is the interest rate per period, and $n$ is the total number of periods.Given:- $P = $600$- Annual interest rate = 7%, so the quarterly interest rate $r = \frac{7\%}{4} = 1.75\%$- $n = 8 \times 4 = 32$ quartersFirst, convert the interest rate to decimal form: $r = 1.75\% = 0.0175$.Plugging the values into the formula:$$FV_{\text{annuity due}} = 600 \times \left( \frac{(1 + 0.0175)^{32} - 1}{0.0175} \right) \times (1 + 0.0175)$$$$FV_{\text{annuity due}} \approx 600 \times 45.48755 \times 1.0175$$$$FV_{\text{annuity due}} \approx 25,892.65$$Therefore, after 8 years, Gail Kelley will have approximately $25,892.65 in her account.

Gail Kelley Deposits $600 in an Account at the Beginning