an account has a principal of $4500 and earns 4.8% interest per year, compounded monthly. no additional…

Explanation:

Step1: Identify compound - interest formula

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

Given $P = 4500$, $r=0.048$ (since $4.8%=0.048$), $n = 12$ (compounded monthly), and $t=\frac{18}{12}=1.5$ years.

Step3: Substitute values into the formula

$A = 4500(1+\frac{0.048}{12})^{12\times1.5}$. First, calculate $\frac{0.048}{12}=0.004$. Then $1+\frac{0.048}{12}=1 + 0.004=1.004$. And $12\times1.5 = 18$. So $A = 4500\times(1.004)^{18}$.

Step4: Calculate $(1.004)^{18}$

Using a calculator, $(1.004)^{18}\approx1.074637$.

Step5: Calculate the final amount

$A = 4500\times1.074637\approx4835.87$.

Answer:

$4835.87$