Question

if you borrow $500 for 10 years at an annual interest rate of 30%, what is the total amount of money you will pay back?

Explanation:

Step1: Identify the formula for compound interest

The formula for compound interest is $A = P(1 + r)^t$, 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 (decimal), and $t$ is the time the money is invested or borrowed for, in years.

Step2: Convert the interest rate to decimal

The annual interest rate is 30%, so in decimal form, $r = \frac{30}{100} = 0.3$.

Step3: Substitute the values into the formula

We have $P = 500$, $r = 0.3$, and $t = 10$. Substituting these into the formula $A = P(1 + r)^t$, we get:
$A = 500(1 + 0.3)^{10}$

Step4: Calculate $(1 + 0.3)^{10}$

First, calculate $1 + 0.3 = 1.3$. Then, calculate $1.3^{10}$. Using a calculator, $1.3^{10} \approx 13.7858491849$.

Step5: Calculate the final amount

Multiply this result by the principal amount: $A = 500 \times 13.7858491849 \approx 6892.92$.

Answer:

The total amount of money to be paid back is approximately $\$6892.92$.