1. **Problem Statement:** A bill of exchange for 500000 dated January 15, 2024, is drawn at 90 days after sight. It was accepted on January 20, 2024. We need to find: a) Due date considering 3 days grace b) Discounted value on February 1, 2024, at 10% p.a. c) Banker's commission at 0.5% d) Net proceeds to the holder 2. **Key formulas and rules:** - Due date = Acceptance date + 90 days + 3 days grace - Discount period = Due date - Discount date - Discount = Principal × Rate × Time (in years) - Banker's commission = Principal × Commission rate - Net proceeds = Principal - Discount - Commission 3. **Step a) Calculate due date:** Acceptance date = January 20, 2024 Add 90 days: January 20 + 90 days = April 19, 2024 Add 3 days grace: April 19 + 3 days = April 22, 2024 Due date = April 22, 2024 4. **Step b) Calculate discounted value on February 1, 2024:** Discount period = Due date - Discount date = April 22 - February 1 Calculate days between February 1 and April 22: February (29 days in 2024, leap year) - 1 = 28 days March = 31 days April = 22 days Total = 28 + 31 + 22 = 81 days Discount rate = 10% p.a. = 0.10 Time in years = $\frac{81}{365}$ Discount = Principal × Rate × Time = 500000 × 0.10 × $\frac{81}{365}$ = 500000 × 0.10 × 0.2219 = 11095 Discounted value = Principal - Discount = 500000 - 11095 = 488905 5. **Step c) Calculate banker's commission:** Commission rate = 0.5% = 0.005 Commission = Principal × Commission rate = 500000 × 0.005 = 2500 6. **Step d) Calculate net proceeds:** Net proceeds = Discounted value - Commission = 488905 - 2500 = 486405 **Final answers:** a) Due date = April 22, 2024 b) Discounted value = 488905 c) Banker's commission = 2500 d) Net proceeds = 486405