1. **State the problem:** We need to find the principal amount $P$ that must be invested to earn $314.10$ in interest in 5 years at an interest rate of 9% per year. 2. **Identify the formula:** Assuming the interest is simple interest, use the formula: $$I = P \times r \times t$$ where $I$ is the interest, $r$ is the rate per year, and $t$ is the time in years. 3. **Plug in known values:** $$314.10 = P \times 0.09 \times 5$$ 4. **Solve for $P$: ** $$P = \frac{314.10}{0.09 \times 5} = \frac{314.10}{0.45} = 698$$ 5. **Interpretation:** The principal amount that must be invested is $698$ to earn $314.10$ in 5 years at 9% simple interest.