find the final amount of money in an account if $8,500 is deposited at 7.5% interest compounded monthly and…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the final amount, $P$ 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 the given values to the appropriate form

Given $P = 8500$, $r=0.075$ (since $7.5%= 0.075$), $n = 12$ (compounded monthly), and $t = 8$.

Step3: Substitute the values into the formula

$A=8500(1 +\frac{0.075}{12})^{12\times8}$. 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: $12\times8 = 96$. So, $A = 8500\times(1.00625)^{96}$.

Step4: Calculate $(1.00625)^{96}$

Using a calculator, $(1.00625)^{96}\approx1.818043$.

Step5: Calculate the final amount $A$

$A=8500\times1.818043\approx15453.37$.

Answer:

$15453.37$