use the compound interest formula to compute the total amount accumulated and the interest earned. $6500 for…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. Given $P = 6500$, $r=0.075$ (since $7.5%=0.075$), $n = 12$ (compounded monthly), and $t = 2$.

Step2: Substitute values into formula

$A=6500(1 +\frac{0.075}{12})^{12\times2}$ First, calculate the value inside the parentheses: $\frac{0.075}{12}=0.00625$, then $1+\frac{0.075}{12}=1 + 0.00625=1.00625$. Next, calculate the exponent: $12\times2 = 24$. So, $A = 6500\times(1.00625)^{24}$.

Step3: Calculate $(1.00625)^{24}$

Using a calculator, $(1.00625)^{24}\approx1.161184$.

Step4: Calculate $A$

$A=6500\times1.161184 = 7547.696\approx7547.70$

Answer:

$7547.70$