Question

katelyn’s older brother borrowed money for school. he took out a loan that charges 6% simple interest. he will end up paying $720 in interest after 6 years. how much did katelyn’s brother borrow for school?

Explanation:

Step1: Recall simple interest formula

The formula for simple interest is $I = P \times r \times t$, where $I$ is the interest, $P$ is the principal (the amount borrowed), $r$ is the annual interest rate (in decimal form), and $t$ is the time in years.

Step2: Convert the interest rate to decimal

The interest rate $r$ is 6%, which in decimal form is $r = \frac{6}{100}= 0.06$.

Step3: Substitute the known values into the formula and solve for $P$

We know that $I = 720$, $r = 0.06$, and $t = 6$. Substituting these into the formula $I = P \times r \times t$, we get:
$$720 = P \times 0.06 \times 6$$
First, calculate $0.06\times6 = 0.36$. So the equation becomes:
$$720 = P \times 0.36$$
To solve for $P$, we divide both sides of the equation by $0.36$:
$$P=\frac{720}{0.36}$$
$$P = 2000$$

Answer:

Katelyn's brother borrowed $\$2000$ for school.