1. **State the problem:** We need to find the principal amount of a loan that amounts to 56,700 after 3 years with a simple interest rate of 9% per year. 2. **Formula for simple interest:** $$ A = P + I $$ where $A$ is the amount, $P$ is the principal, and $I$ is the interest. The interest $I$ is calculated as: $$ I = P \times r \times t $$ where $r$ is the rate (in decimal) and $t$ is the time in years. 3. **Substitute the interest formula into the amount formula:** $$ A = P + P \times r \times t = P(1 + rt) $$ 4. **Plug in the known values:** $$ 56,700 = P(1 + 0.09 \times 3) $$ 5. **Simplify inside the parentheses:** $$ 56,700 = P(1 + 0.27) = P(1.27) $$ 6. **Solve for $P$ by dividing both sides by 1.27:** $$ P = \frac{56,700}{1.27} $$ 7. **Show cancellation for clarity:** $$ P = \frac{56,700}{\cancel{1.27}} \times \frac{\cancel{1}}{1} $$ 8. **Calculate the principal:** $$ P = 44,645.67 $$ **Final answer:** The principal amount is $44,645.67$.