For 7 years, Thompson Cleaners deposits $800 at the end of each quarter into an account paying 8% compounded quarterly. What is the value of the account at the end of 7 years?
A) $29,654.32
B) $29,627.62
C) $28,552.97
D) $29,632.97
E) $29,640.97

Question

For 7 years, Thompson Cleaners deposits $800 at the end of each quarter into an account paying 8% compounded quarterly. What is the value of the account at the end of 7 years? ​
A) $29,654.32
B) $29,627.62
C) $28,552.97
D) $29,632.97
E) $29,640.97

Quizplus · Accepted Answer

The value of the account can be calculated using the future value of an annuity formula: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment per period, $r$ is the interest rate per period, and $n$ is the total number of payments. Here, $P = $800$, $r = 0.08/4 = 0.02$ (since the interest is compounded quarterly), and $n = 7 \times 4 = 28$ (since there are 4 quarters in a year and the deposits are made for 7 years). Plugging these values into the formula gives $FV = 800 \times \frac{(1 + 0.02)^{28} - 1}{0.02}$, which calculates to approximately $29,640.97.

For 7 Years, Thompson Cleaners Deposits $800 at the End