Question

Use the compound interest formula to compute the total amount accumulated and the interest earned.$4000 for 4 years at 2.6% compounded monthlyThe total amount accumulated after 4 years is $(Round to the nearest cent as needed.)

Answer 1

The compound interest formula is given by

$A=P(1+\frac{r}{n})^{nt}$

Where A represents the amount accumulated, P represents the initial amount, r is the interest rate, n is the number of times the interest is compounded per unit t(in our case, a year), and t represents the time.

From the text, we have the following values:

$\begin{gathered} P=4000 \\ r=0.026 \\ n=12 \\ t=4 \end{gathered}$

Just plugging those values in our formula, we have

$\begin{gathered} A=4000(1+\frac{0.026}{12})^{12\times4} \\ A=4000(1+\frac{0.026}{12})^{48}=4437.90252\approx4437.90 \end{gathered}$

The total accumulated after 4 years is $4437.90.