Question

elsa borrowed $8000 at a rate of 8%, compounded quarterly. assuming she makes no payments, how much will she owe after 7 years? do not round any intermediate computations, and round your answer to the nearest cent.

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 $P=\$8000$, $r = 8\%=0.08$, $n = 4$ (compounded quarterly), and $t = 7$ years.

Step3: Substitute values into the formula

$A=8000(1 +\frac{0.08}{4})^{4\times7}=8000(1 + 0.02)^{28}$.

Step4: Calculate the value inside the parentheses

$(1 + 0.02)^{28}$. Using a calculator, $(1.02)^{28}\approx1.741024$.

Step5: Calculate the final amount

$A = 8000\times1.741024=\$13928.192$.

Answer:

$13928.19$