1. **State the problem:** We need to find the principal amount $P$ that, when invested at an interest rate of 4.5% per year, will earn $750 in 10 months. 2. **Formula used:** For simple interest, the interest earned $I$ is given by the formula: $$I = P \times r \times t$$ where $r$ is the annual interest rate (in decimal), and $t$ is the time in years. 3. **Convert given values:** - Interest earned $I = 750$ - Annual interest rate $r = 4.5\% = 0.045$ - Time $t = \frac{10}{12} = \frac{5}{6}$ years 4. **Substitute values into the formula:** $$750 = P \times 0.045 \times \frac{5}{6}$$ 5. **Solve for $P$:** $$P = \frac{750}{0.045 \times \frac{5}{6}}$$ 6. **Simplify denominator:** $$0.045 \times \frac{5}{6} = 0.045 \times 0.8333... = 0.0375$$ 7. **Calculate $P$:** $$P = \frac{750}{0.0375}$$ 8. **Final calculation:** $$P = 20000$$ **Answer:** The principal needed to invest is **20000.00** (rounded to the nearest cent).