suppose that $2000 is loaned at a rate of 6%, compounded monthly. assuming that no payments are made, find…

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.

Step2: Convert values to appropriate form

Given $P=$2000$, $r = 6%=0.06$, $n = 12$ (compounded monthly), and $t = 10$ years.

Step3: Substitute values into formula

$A=2000(1 +\frac{0.06}{12})^{12\times10}$. First, calculate the value inside the parentheses: $\frac{0.06}{12}=0.005$, then $1+\frac{0.06}{12}=1 + 0.005=1.005$. Next, calculate the exponent: $12\times10 = 120$. So, $A = 2000\times(1.005)^{120}$.

Step4: Calculate the final amount

Using a calculator, $(1.005)^{120}\approx1.819396734$. Then $A=2000\times1.819396734=$3638.793468$. Rounding to the nearest cent, $A\approx$3638.79$.

Answer:

$$3638.79$