1. **State the problem:** Shelly Katz gave Ron Prentice a $4,400 note at 6% interest for 165 days. On May 10, Shelly discounted the note at Roseville Bank at 10%. We need to find the proceeds Shelly receives. 2. **Identify key dates and terms:** - Note amount (principal) $P = 4400$ - Note interest rate $r = 6\% = 0.06$ - Note term $t = 165$ days - Bank discount rate $d = 10\% = 0.10$ - Use 360 days per year 3. **Calculate maturity value of the note:** The maturity value $M$ is principal plus interest: $$M = P + I = P + P \times r \times \frac{t}{360} = P \left(1 + r \frac{t}{360}\right)$$ Calculate interest: $$I = 4400 \times 0.06 \times \frac{165}{360} = 4400 \times 0.06 \times 0.4583333 = 121.00$$ Calculate maturity value: $$M = 4400 + 121 = 4521$$ 4. **Calculate days from discount date (May 10) to maturity date:** Note date: Feb 26 Note term: 165 days Maturity date = Feb 26 + 165 days Calculate days from Feb 26 to May 10: - Feb 26 to Feb 28 = 2 days - Mar = 30 days - Apr = 30 days - May 1 to May 10 = 10 days Total = 2 + 30 + 30 + 10 = 72 days Days remaining from May 10 to maturity: $$165 - 72 = 93$$ days 5. **Calculate bank discount on maturity value:** Bank discount $D$ is: $$D = M \times d \times \frac{\text{days remaining}}{360} = 4521 \times 0.10 \times \frac{93}{360}$$ Calculate: $$D = 4521 \times 0.10 \times 0.2583333 = 116.79$$ 6. **Calculate proceeds Shelly receives:** Proceeds = Maturity value - Bank discount $$\text{Proceeds} = 4521 - 116.79 = 4404.21$$ **Final answer:** Shelly Katz receives $4404.21$ as proceeds from the bank discount.