use the appropriate compound interest formula to compute the balance in the account after the stated period…

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 percentage rate (APR) 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 given values to appropriate form

We have $P=$3000$, $r = 0.05$ (since $5%=0.05$), $n = 12$ (monthly compounding), and $t = 12$ years.

Step3: Substitute values into the formula

$A=3000(1 +\frac{0.05}{12})^{12\times12}$. First, calculate the value inside the parentheses: $\frac{0.05}{12}\approx0.004167$, then $1+\frac{0.05}{12}=1 + 0.004167=1.004167$. Next, calculate the exponent: $12\times12 = 144$. So, $A = 3000\times(1.004167)^{144}$. Using a calculator, $(1.004167)^{144}\approx1.819397$. Then $A=3000\times1.819397 = 5458.191$.

Step4: Round the result

Rounding to the nearest cent, $A\approx$5458.19$.

Answer:

$5458.19$