suppose that $45,300 is invested in a certificate of deposit for 1 year at 10.1% annual interest to be…

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. Here, $P = 45300$, $r=0.101$, $n = 2$ (semi - annual compounding), and $t = 1$.

Step2: Calculate the amount $A$

Substitute the values into the formula: $A=45300(1 +\frac{0.101}{2})^{2\times1}$. First, calculate the value inside the parentheses: $\frac{0.101}{2}=0.0505$, then $1 + 0.0505=1.0505$. Next, calculate $(1.0505)^{2}=1.10355025$. Then, $A = 45300\times1.10355025=49990.826325$.

Step3: Calculate the interest earned

The interest earned $I=A - P$. So, $I=49990.826325−45300 = 4690.826325\approx4690.83$.

Answer:

$4690.83$