find the final amount of money in an account if $5,800 is deposited at 6.5% 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 correct form

Given $P = 5800$, $r=0.065$ (since $6.5%=0.065$), $n = 12$ (compounded monthly), and $t = 10$.

Step3: Substitute the values into the formula

$A=5800(1 +\frac{0.065}{12})^{12\times10}$. First, calculate the value inside the parentheses: $\frac{0.065}{12}\approx0.0054167$, then $1+\frac{0.065}{12}=1 + 0.0054167=1.0054167$. Next, calculate the exponent: $12\times10 = 120$. So, $A = 5800\times(1.0054167)^{120}$.

Step4: Calculate $(1.0054167)^{120}$

Using a calculator, $(1.0054167)^{120}\approx1.915493$.

Step5: Calculate the final amount $A$

$A=5800\times1.915493\approx11009.86$.

Answer:

$11009.86$