an investment of $8,350 earns 5.2% interest compounded monthly over 10 years. approximately how much…

Answer:

C. $5,679

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), $n$ 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 amount $A$

$A=8350(1 +\frac{0.052}{12})^{12\times10}$ First, calculate the value inside the parentheses: $\frac{0.052}{12}\approx0.004333$. Then $1+\frac{0.052}{12}=1 + 0.004333=1.004333$. Next, calculate the exponent: $12\times10 = 120$. So, $A = 8350\times(1.004333)^{120}$. Using a calculator, $(1.004333)^{120}\approx1.6860$. Then $A=8350\times1.6860=$14029$.

Step3: Calculate the interest earned

The interest earned $I=A - P$. $I=14029 - 8350=$5679$.