dan borrowed $8000 at a rate of 12.5%, 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=$8000$, $r = 12.5%=0.125$, $n = 2$ (compounded semiannually), and $t = 8$ years.

Step3: Substitute values into formula

$A=8000(1 +\frac{0.125}{2})^{2\times8}=8000(1 + 0.0625)^{16}$.

Step4: Calculate the value inside the parentheses

$1+0.0625 = 1.0625$.

Step5: Calculate the exponentiation

$(1.0625)^{16}\approx2.685063838$.

Step6: Calculate the final amount

$A = 8000\times2.685063838=$21480.510704\approx$21480.51$.

Answer:

$21480.51$