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

Problem: Eduardo noticed that his new car loan papers stated that with a $7.5\%$ simple interest rate, he would pay $\$6{,}596.25$ in interest over $5$ years. How much did he borrow to pay for his car?

1. Read the problem carefully.
2. Identify what to find: the amount borrowed (the principal).
3. Name the unknown: Let $P$ = principal borrowed.
4. Translate into an equation using the simple interest formula $I = Prt$. Given $I = 6{,}596.25$, $r = 0.075$, and $t = 5$: $6{,}596.25 = P(0.075)(5)$
5. Solve the equation: Multiply $0.075$ and $5$: $6{,}596.25 = 0.375P$ Divide both sides by $0.375$: $17{,}590 = P$
6. Check the result: $I = Prt$ $6{,}596.25 \stackrel{?}{=} (17{,}590)(0.075)(5)$ $6{,}596.25 = 6{,}596.25 \checkmark$
7. Answer: The principal was $\$17{,}590$.