an investment of $9,875 earns 4.8% interest compounded monthly over 12 years. approximately how much…

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=$9875$, $r = 0.048$ (since $4.8%=0.048$), $n = 12$ (compounded monthly), and $t = 12$ years.

Step2: Calculate the amount $A$

$A=9875(1 +\frac{0.048}{12})^{12\times12}=9875(1 + 0.004)^{144}=9875\times1.004^{144}$. First, calculate $1.004^{144}$. Using a calculator, $1.004^{144}\approx1.7029$. Then $A = 9875\times1.7029\approx16725$.

Step3: Calculate the interest earned

The interest earned $I=A - P$. So $I=16725-9875 = 6850$. The closest answer to $6850$ is $$7458$.

Answer:

B. $7,458$