an investment of $6,530 earns interest at the rate of 4% and is compounded quarterly. what is the…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the accumulated value, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.

Step2: Convert values to appropriate form

Given $P = 6530$, $r=0.04$ (since $4%=0.04$), $n = 4$ (compounded quarterly), and $t = 8$.

Step3: Substitute values into formula

$A=6530(1 +\frac{0.04}{4})^{4\times8}=6530(1 + 0.01)^{32}$.

Step4: Calculate the value inside the parentheses

$(1 + 0.01)^{32}=1.01^{32}$. Using a calculator, $1.01^{32}\approx1.370101$.

Step5: Calculate the accumulated value

$A = 6530\times1.370101\approx8946.76$.

Answer:

C. $$8,936.76$