deon borrowed $8000 at a rate of 8%, compounded semiannually. assuming he makes no payments, how much will…

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=$8000$, $r = 8%=0.08$, $n = 2$ (compounded semiannually), and $t = 6$ years.

Step3: Substitute values into formula

$A=8000(1 +\frac{0.08}{2})^{2\times6}=8000(1 + 0.04)^{12}$.

Step4: Calculate the value

First, calculate $(1 + 0.04)^{12}$. Using a calculator, $(1 + 0.04)^{12}\approx1.601032219$. Then, $A = 8000\times1.601032219\approx12808.26$.

Answer:

$12808.26$