an investment of $8,350 earns 5.2% interest c...

# 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, $P=\$8350$, $r = 0.052$, $n = 12$ (monthly compounding), and $t = 10$. ## Step2: Calculate the value of $(1+\frac{r}{n})^{nt}$ First, calculate $\frac{r}{n}=\frac{0.052}{12}\approx0.004333$. Then, $nt=12\times10 = 120$. So, $(1+\frac{0.052}{12})^{120}=(1 + 0.004333)^{120}$. Using a calculator, $(1.004333)^{120}\approx1.6865$. ## Step3: Calculate the final amount $A$ $A=P(1+\frac{r}{n})^{nt}=8350\times1.6865\approx14082.275$. ## Step4: Calculate the interest earned The interest earned $I=A - P$. So, $I=14082.275−8350=\$5732.275\approx\$5679$ (closest to the given options). # Answer: C. $5,679