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

Problem: In $5$ years, Gloria’s bank account earned $\$2{,}400$ interest at $5\%$ simple interest. How much had she deposited in the account?

1. Read the problem carefully.
2. Identify what to find: the amount deposited (the principal).
3. Name the unknown: Let $P$ = principal deposited.
4. Translate into an equation using the simple interest formula $I = Prt$. Given $I = 2400$, $r = 0.05$, and $t = 5$: $2400 = P(0.05)(5)$
5. Solve the equation: Multiply $0.05$ and $5$: $2400 = 0.25P$ Divide both sides by $0.25$: $9{,}600 = P$
6. Check the result: $I = Prt$ $2400 \stackrel{?}{=} (9{,}600)(0.05)(5)$ $2400 = 2400 \checkmark$
7. Answer: The principal was $\$9{,}600$.