an investment of $7,650 earns interest at the rate of 5% 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 $P$ 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=$7650$, $r = 0.05$ (since $5%=0.05$), $n = 4$ (compounded quarterly), and $t = 9$ years.

Step3: Substitute values into the formula

$A=7650(1 +\frac{0.05}{4})^{4\times9}=7650(1 + 0.0125)^{36}$.

Step4: Calculate the value inside the parentheses

$1+0.0125=1.0125$.

Step5: Calculate the exponentiation

$(1.0125)^{36}\approx1.564205$.

Step6: Calculate the final amount

$A = 7650\times1.564205\approx11964.17$.

Answer:

A. $11,964.17$