select the correct answer. calculate the compound amount. round to the nearest cent for, p = $3000, r = 5%…

Explanation:

Step1: Identify the 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.

Step2: Convert the given values to the appropriate form

Given $P = 3000$, $r=0.05$ (since $5%=0.05$), $n = 12$ (compounded monthly), and $t = 5$.

Step3: Substitute the values into the formula

$A=3000(1 +\frac{0.05}{12})^{12\times5}=3000(1+\frac{0.05}{12})^{60}$. First, calculate $1+\frac{0.05}{12}=1+\frac{1}{240}=\frac{240 + 1}{240}=\frac{241}{240}\approx1.004167$. Then, $(1.004167)^{60}\approx1.28335$. Finally, $A = 3000\times1.28335=3850.05$. Rounding to the nearest cent, $A\approx3850.06$.

Answer:

B. $3850.06$