suppose that $2000 is invested at a rate of 3.7%, compounded semiannually. assuming that no withdrawals are…

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=$2000$, $r = 3.7%=0.037$, $n = 2$ (compounded semiannually), and $t = 4$ years.

Step3: Substitute values into the formula

$A=2000(1 +\frac{0.037}{2})^{2\times4}=2000(1 + 0.0185)^{8}$.

Step4: Calculate the value inside the parentheses

$1+0.0185 = 1.0185$.

Step5: Calculate the exponentiation

$(1.0185)^{8}\approx1.15779$.

Step6: Calculate the final amount

$A = 2000\times1.15779=$2315.58$.

Answer:

$2315.58$