Question

Hang borrowed \($7500$from her parents to pay her tuition. In $5$years, she paid them \)$1500$interest in addition to the $$7500$ she borrowed. What was the rate of interest?

Short answer

Hang borrowed $$7500$ from her parents to pay her tuition. In $5$years, she paid them $$1500$ interest then the rate of interest was$4\%$

Step-by-step solution

Step 1. Given information  

principal$P=\$7500$

Simple Interest$I=\$1500$

Time$t=5$

Step 2. Interest rate 

Consider the interest rate is r

Substitute principal, simple interest, and time in Simple interest formula

$$\begin{gathered} I=Prt \\ 1500=\left(7500\right)\left(i\right)\left(5\right) \\ 1500=37500i \\ \frac{1500}{37500}=i \\ 0.04=i \\ i=4\% \end{gathered}$$

So the interest rate was$4\%$

Step 3. Verification 

With an interest rate of $4$% and a time of $5$years, $ $1500$is the simple interest of the principal

$$\begin{gathered} I=Prt \\ 1500=P(0.04)\left(5\right) \\ 1500=0.20P \\ \frac{1500}{0.20}=7500 \end{gathered}$$

Principal is$7500$

so the interest rate$4\%$is correct.