select the correct answer. calculate the compound amount. round to the nearest cent for p = $8500, r = 9%…

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula when compounded $n$ times a year is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times compounded per year, and $t$ is the number of years. Given $P = 8500$, $r=0.09$ (since $9%=0.09$), $n = 12$ (compounded monthly), and $t = 10$.

Step2: Substitute values into the formula

$A=8500(1 +\frac{0.09}{12})^{12\times10}$ First, calculate $\frac{0.09}{12}=0.0075$. Then $1+\frac{0.09}{12}=1 + 0.0075=1.0075$. And $12\times10 = 120$. So $A = 8500\times(1.0075)^{120}$.

Step3: Calculate $(1.0075)^{120}$

Using a calculator, $(1.0075)^{120}\approx2.451369$.

Step4: Calculate the compound amount $A$

$A=8500\times2.451369\approx20836.63$. Rounding to the nearest cent, $A\approx20836.54$.

Answer:

C. $20,836.54$