dante borrowed $8000 at a rate of 19.5%, compounded semiannually. assuming he makes no payments, how much…

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 or borrowed for in years.

Step2: Convert given values to correct form

We have $P=$8000$, $r = 0.195$ (since $19.5%=0.195$), $n = 2$ (compounded semiannually), and $t = 10$ years.

Step3: Substitute values into formula

$A=8000(1 +\frac{0.195}{2})^{2\times10}=8000(1 + 0.0975)^{20}$.

Step4: Calculate the value inside the parentheses

$1+0.0975 = 1.0975$.

Step5: Calculate the exponentiation

$(1.0975)^{20}\approx6.08108$.

Step6: Calculate the final amount

$A = 8000\times6.08108=$48648.64$.

Answer:

$48648.64$