1. **State the problem:** Shelly Katz gave Ron Prentice a $4,400 note at 6% interest for 165 days on Feb. 26. 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 - Discount rate $d = 10\% = 0.10$ - Year length = 360 days - Date note given: Feb 26 - Date discounted: May 10 3. **Calculate maturity date:** - Maturity date = Feb 26 + 165 days - Days in months (using 360-day year approximation): Feb 26 to Mar 26 = 30 days Mar 26 to Apr 26 = 30 days Apr 26 to May 26 = 30 days - Total 90 days to May 26, so 165 - 90 = 75 days after May 26 - Maturity date = May 26 + 75 days = Aug 9 4. **Calculate days from discount date to maturity date:** - May 10 to Aug 9 = 31 (May 10 to Jun 10) + 30 (Jun 10 to Jul 10) + 30 (Jul 10 to Aug 9) = 91 days 5. **Calculate maturity value of the note:** $$M = P + I = P + P \times r \times \frac{t}{360} = 4400 + 4400 \times 0.06 \times \frac{165}{360}$$ $$= 4400 + 4400 \times 0.06 \times 0.4583333 = 4400 + 121.00 = 4521.00$$ 6. **Calculate bank discount:** $$D = M \times d \times \frac{\text{days from discount to maturity}}{360} = 4521 \times 0.10 \times \frac{91}{360}$$ $$= 4521 \times 0.10 \times 0.2527777 = 114.27$$ 7. **Calculate proceeds Shelly receives:** $$\text{Proceeds} = M - D = 4521.00 - 114.27 = 4406.73$$ **Final answer:** Shelly Katz receives proceeds of **4406.73** dollars.