Question

find the compound amount for the deposit and the amount of interest earned. $6700 at 8.2% compounded quarterly for 5 years. identify the formula needed to find the compound amount and substitute the appropriate values into it. select the correct answer and fill in the answer boxes to complete your choice. a fv = 6700(1 + \frac{0.082}{4})^{20} b fv = c fv = 1 + 0.082( ). the compound amount after 5 years is $ (do not round until the final answer. then round to the nearest cent as needed.)

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $FV = PV(1+\frac{r}{n})^{nt}$, where $PV$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times compounded per year, and $t$ is the number of years. Here, $PV=\$6700$, $r = 0.082$, $n = 4$ (compounded quarterly), and $t = 5$.

Step2: Substitute values into the formula

$FV=6700(1 +\frac{0.082}{4})^{4\times5}=6700(1 + 0.0205)^{20}$.

Step3: Calculate the value inside the parentheses

$1+0.0205=1.0205$.

Step4: Calculate the exponent part

$(1.0205)^{20}\approx1.485947$.

Step5: Calculate the future value

$FV = 6700\times1.485947\approx9955.84$.

Answer:

The correct formula is A. $FV = 6700(1+\frac{0.082}{4})^{20}$. The compound amount after 5 years is $\$9955.84$.