Question

find the compound amount for the deposit and the amount of interest earned. $5700 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 = □(1 + \frac{0.082}{□})^{□} b. fv = □e^{0.082(□)} c. fv = 57001 + 0.082(5)

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula when compounded $n$ times a year 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, $PV=\$5700$, $r = 0.082$, $n = 4$ (compounded quarterly), and $t = 5$.

Step2: Substitute values into the formula

$FV=5700(1 +\frac{0.082}{4})^{4\times5}=5700(1 + 0.0205)^{20}$.
First, calculate the value inside the parentheses: $1+0.0205 = 1.0205$.
Then, find $(1.0205)^{20}\approx1.485947$.
Finally, $FV=5700\times1.485947\approx8469.90$.
The interest earned $I=FV - PV=8469.90 - 5700=\$2769.90$.

Answer:

The compound amount $FV\approx\$8469.90$ and the interest earned $I\approx\$2769.90$. The correct formula for compound - interest (from the multiple - choice part) is $FV = PV(1+\frac{r}{n})^{nt}$, which in the given options would be filled as $FV=5700(1+\frac{0.082}{4})^{20}$ (Option A with $PV = 5700$, $n = 4$, and $nt=20$).