diane borrowed $8000 at a rate of 15%, compounded monthly. assuming she makes no payments, how much will she…

Explanation:

Step1: Identify the 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 the given values to the appropriate form

We are given that $P=$8000$, $r = 15%=0.15$, $n = 12$ (compounded monthly), and $t = 6$ years.

Step3: Substitute the values into the formula

$A=8000(1 +\frac{0.15}{12})^{12\times6}$. First, calculate the value inside the parentheses: $\frac{0.15}{12}=0.0125$, then $1+\frac{0.15}{12}=1 + 0.0125=1.0125$. Next, calculate the exponent: $12\times6 = 72$. So, $A = 8000\times(1.0125)^{72}$.

Step4: Calculate the final amount

Using a calculator, $(1.0125)^{72}\approx2.443219$. Then $A=8000\times2.443219=$19545.752$. Rounding to the nearest cent, $A\approx$19545.75$.

Answer:

$19545.75$