1. **State the problem:** We need to find the face value (principal) of a 90-day promissory note given the maturity value and the annual interest rate. 2. **Formula used:** The maturity value $M$ of an interest-bearing note is given by: $$M = P + I$$ where $P$ is the face value (principal) and $I$ is the interest. Interest $I$ can be calculated using simple interest 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 time to years:** Since the note is for 90 days, $$t = \frac{90}{365}$$ 4. **Express maturity value in terms of $P$:** $$M = P + P \times r \times t = P(1 + r t)$$ 5. **Substitute known values:** $$2345 = P \left(1 + 0.08 \times \frac{90}{365}\right)$$ 6. **Calculate the factor:** $$1 + 0.08 \times \frac{90}{365} = 1 + 0.08 \times 0.246575342 = 1 + 0.019726 = 1.019726$$ 7. **Solve for $P$:** $$P = \frac{2345}{1.019726}$$ 8. **Show cancellation step:** $$P = \frac{\cancel{2345}}{\cancel{1.019726}}$$ 9. **Calculate $P$:** $$P \approx 2298.53$$ **Final answer:** The face value of the note is approximately 2298.53.