Apply the problem-solving strategy to find the rate of simple interest given the principal, interest earned, and time.

Problem: Jim lent his sister $\$5{,}000$ to help her buy a house. In $3$ years, she paid him the $\$5{,}000$, plus $\$900$ interest. What was the rate of simple interest?

1. Read the problem carefully.
2. Identify what to find: the rate of simple interest.
3. Name the unknown: Let $r$ = rate of interest.
4. Translate into an equation using the simple interest formula $I = Prt$. Given $I = 900$, $P = 5{,}000$, and $t = 3$: $900 = (5{,}000)r(3)$
5. Solve the equation: Multiply $5{,}000$ and $3$: $900 = 15{,}000r$ Divide both sides by $15{,}000$: $0.06 = r$ Change the decimal to percent form: $6\% = r$
6. Check the result: $I = Prt$ $900 \stackrel{?}{=} (5{,}000)(0.06)(3)$ $900 = 900 \checkmark$
7. Answer: The rate of interest was $6\%$.