suppose that $2000 is invested at a rate of 3.9%, compounded quarterly. assuming that no withdrawals are…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years.

Step2: Convert given values to appropriate form

Given $P=$2000$, $r = 3.9%=0.039$, $n = 4$ (compounded quarterly), and $t = 9$ years.

Step3: Substitute values into the formula

$A=2000(1 +\frac{0.039}{4})^{4\times9}$. First, calculate the value inside the parentheses: $\frac{0.039}{4}=0.00975$, then $1+\frac{0.039}{4}=1 + 0.00975=1.00975$. Next, calculate the exponent: $4\times9 = 36$. So, $A = 2000\times(1.00975)^{36}$.

Step4: Calculate the final amount

Using a calculator, $(1.00975)^{36}\approx1.401977$. Then $A=2000\times1.401977 = 2803.954$. Rounding to the nearest cent, $A\approx$2803.95$.

Answer:

$$2803.95$