destiny is going to start a planned savings to save up for a new car. she can afford to save 5% of her gross…

Explanation:

Step1: Calculate the annual savings

First, find out how much she saves in a year. Her gross income is $4400$ and she saves 5% of it. So the annual - savings $P$ is $P = 4400\times0.05\times12=4400\times0.6 = 2640$.

Step2: Identify the compound - interest formula variables

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. Here, $P = 2640$, $r=0.045$ (since 4.5%=0.045), $n = 12$ (compounded monthly), and $t = 1$.

Step3: Calculate the amount in the account after one year of compounding

Substitute the values into the formula: [ \begin{align*} A&=2640(1+\frac{0.045}{12})^{12\times1}\ &=2640(1 + 0.00375)^{12}\ &=2640\times(1.00375)^{12} \end{align*} ] Using a calculator, $(1.00375)^{12}\approx1.04588$. Then $A = 2640\times1.04588\approx2761.28$.

Answer:

$2,761.28$