suppose that $2000 is invested at a rate of 5.4%, 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 interest is compounded per year, and $t$ is the number of years.

Step2: Convert values to appropriate form

Given $P=$2000$, $r = 5.4%=0.054$, $n = 12$ (compounded monthly), and $t = 8$ years.

Step3: Substitute values into formula

$A=2000(1 +\frac{0.054}{12})^{12\times8}$. First, calculate $\frac{0.054}{12}=0.0045$. Then $1+\frac{0.054}{12}=1 + 0.0045=1.0045$. And $12\times8 = 96$. So $A = 2000\times(1.0045)^{96}$.

Step4: Calculate the value of $(1.0045)^{96}$

Using a calculator, $(1.0045)^{96}\approx1.539997$.

Step5: Calculate the final amount $A$

$A=2000\times1.539997=$3079.994\approx$3079.99$.

Answer:

$$3079.99$