suppose that $2000 is invested at a rate of 2.4%, 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 given values

Given $P=$2000$, $r = 2.4%=0.024$, $n = 12$ (compounded monthly), and $t = 5$ years.

Step3: Substitute values into formula

$A=2000(1 +\frac{0.024}{12})^{12\times5}$. First, calculate the value inside the parentheses: $\frac{0.024}{12}=0.002$, then $1+\frac{0.024}{12}=1 + 0.002=1.002$. Next, calculate the exponent: $12\times5 = 60$. So, $A = 2000\times(1.002)^{60}$.

Step4: Calculate the final amount

$(1.002)^{60}\approx1.12716014$. Then $A=2000\times1.12716014=$2254.32028$. Rounding to the nearest cent, $A\approx$2254.32$.

Answer:

$2254.32$