isabel borrowed $8000 at a rate of 8.5%, compounded quarterly. assuming she 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=$8000$, $r = 8.5%=0.085$, $n = 4$ (compounded quarterly), and $t = 6$ years.

Step3: Substitute values into formula

$A=8000(1 +\frac{0.085}{4})^{4\times6}=8000(1 + 0.02125)^{24}$.

Step4: Calculate the value inside the parentheses

$1+0.02125 = 1.02125$.

Step5: Calculate the exponentiation

$(1.02125)^{24}\approx1.612707$.

Step6: Calculate the final amount

$A = 8000\times1.612707=$12901.66$.

Answer:

$12901.66$