maureen takes out a loan with a compound interest rate of 6%. if maureen borrows $3000 for 11 years…

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, $P = 3000$, $r=0.06$, $n = 12$ (compounded monthly), and $t = 11$.

Step2: Calculate the amount $A$

Substitute the values into the formula: [ \begin{align*} A&=3000\left(1 +\frac{0.06}{12}\right)^{12\times11}\ &=3000(1 + 0.005)^{132}\ &=3000\times(1.005)^{132} \end{align*} ] Using a calculator, $(1.005)^{132}\approx1.90794$. So, $A = 3000\times1.90794= 5723.82$.

Step3: Calculate the interest $I$

The interest $I$ is the difference between the total amount $A$ and the principal $P$. So, $I=A - P$. $I=5723.82-3000 = 2723.82$.

Answer:

$2723.82$