jessica deposited $4000 into an account with 4.5% interest, compounded semiannually. assuming that no…

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 correct form

The principal $P=$4000$, the annual interest rate $r = 4.5%=0.045$, the number of times compounded per year $n = 2$ (since it's compounded semiannually), and the time $t = 4$ years.

Step3: Substitute values into formula

$A=4000(1 +\frac{0.045}{2})^{2\times4}$. First, calculate the value inside the parentheses: $\frac{0.045}{2}=0.0225$, then $1+\frac{0.045}{2}=1 + 0.0225=1.0225$. Next, calculate the exponent: $2\times4 = 8$. So, $A = 4000\times(1.0225)^{8}$.

Step4: Calculate the final amount

$(1.0225)^{8}\approx1.1940522$. Then $A=4000\times1.1940522=$4776.21$.

Answer:

$4776.21$