suppose that $2000 is invested at a rate of 2.9%, 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 correct form

Given $P=$2000$, $r = 2.9%=0.029$, $n = 2$ (compounded semiannually), and $t = 5$ years.

Step3: Substitute values into formula

$A=2000(1 +\frac{0.029}{2})^{2\times5}=2000(1 + 0.0145)^{10}$.

Step4: Calculate the value inside the parentheses

$1+0.0145 = 1.0145$.

Step5: Calculate the exponent part

$(1.0145)^{10}\approx1.154797$.

Step6: Calculate the final amount

$A = 2000\times1.154797=$2309.594\approx$2309.59$.

Answer:

$2309.59$