eve puts $500.00 into an account to use for school expenses. the account earns 13% interest, compounded…

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.

Step2: Convert values to appropriate form

We have $P=$500$, $r = 0.13$ (since $13%=0.13$), $n = 12$ (compounded monthly), and $t = 6$ years.

Step3: Substitute values into the formula

$A=500(1 +\frac{0.13}{12})^{12\times6}$. First, calculate the value inside the parentheses: $\frac{0.13}{12}\approx0.010833$, then $1+\frac{0.13}{12}=1 + 0.010833=1.010833$. Next, calculate the exponent: $12\times6 = 72$. So, $A = 500\times(1.010833)^{72}$. Using a calculator, $(1.010833)^{72}\approx2.19777$. Then $A=500\times2.19777=$1098.885$.

Step4: Round the answer

Rounding $$1098.885$ to the nearest cent gives $$1098.89$.

Answer:

$1098.89$