select the correct answer. calculate the compound amount. round to the nearest cent. p = $500, r = 9%…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ 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.

Step2: Convert values to appropriate form

Given $P = 500$, $r=0.09$ (since $9%=0.09$), $n = 4$ (compounded quarterly), and $t = 6$.

Step3: Substitute values into formula

$A=500(1 +\frac{0.09}{4})^{4\times6}=500(1 + 0.0225)^{24}$.

Step4: Calculate the value inside the parentheses

$1+0.0225=1.0225$.

Step5: Calculate the exponentiation

$(1.0225)^{24}\approx1.70576$.

Step6: Calculate the final amount

$A = 500\times1.70576=852.88$.

Answer:

A. $852.88$