suppose that $2000 is invested at a rate of 2.1%, compounded monthly. assuming that no withdrawals are made…

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 compounded per year, and $t$ is the number of years.

Step2: Convert values to appropriate form

Given $P=$2000$, $r = 2.1%=0.021$, $n = 12$ (compounded monthly), and $t = 7$ years.

Step3: Substitute values into formula

$A=2000(1 +\frac{0.021}{12})^{12\times7}$. First, calculate $\frac{0.021}{12}=0.00175$. Then, $1+\frac{0.021}{12}=1 + 0.00175=1.00175$. Next, $12\times7 = 84$. So, $A = 2000\times(1.00175)^{84}$.

Step4: Calculate the result

$(1.00175)^{84}\approx1.156777$. $A=2000\times1.156777=$2313.554$. Rounding to the nearest cent, $A\approx$2313.55$.

Answer:

$$2313.55$