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

Problem: Sean’s new car loan statement said he would pay $\$4{,}866.25$ in interest from a simple interest rate of $8.5\%$ over $5$ years. How much did he borrow to buy his new 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 $I = 4{,}866.25$, $r = 0.085$, and $t = 5$: $4{,}866.25 = P(0.085)(5)$
5. Solve the equation: Multiply $0.085$ and $5$: $4{,}866.25 = 0.425P$ Divide both sides by $0.425$: $11{,}450 = P$
6. Check the result: $I = Prt$ $4{,}866.25 \stackrel{?}{=} (11{,}450)(0.085)(5)$ $4{,}866.25 = 4{,}866.25 \checkmark$
7. Answer: The principal was $\$11{,}450$.