1. **Problem Statement:** Amy has a 10% interest bearing note dated 3 March 2025 with a term of 120 days. On 15 May 2025, she discounts the note at 8% and receives proceeds of 15392.54. We need to find: i. The maturity date of the note. ii. The maturity value of the note. iii. The bank discount amount. iv. The face value of the note. v. The amount of interest Amy receives. 2. **Step 1: Find the maturity date.** The note is dated 3 March 2025 and has a term of 120 days. Adding 120 days to 3 March 2025: March has 31 days, so days remaining in March after 3rd = 28 days. 120 - 28 = 92 days left. April has 30 days, so 92 - 30 = 62 days left. May has 31 days, so 62 - 31 = 31 days left. June has 30 days, so 31 - 30 = 1 day left. Therefore, maturity date is 1 July 2025. 3. **Step 2: Calculate the maturity value (M).** Formula for maturity value of a note: $$M = F \times \left(1 + r \times \frac{t}{360}\right)$$ where - $F$ = face value - $r$ = interest rate (10% = 0.10) - $t$ = term in days (120) We do not know $F$ yet, so we will find it later. 4. **Step 3: Calculate the discount period and bank discount amount.** Discounting date is 15 May 2025. Days from discount date to maturity date: From 15 May to 1 July: May: 31 - 15 = 16 days June: 30 days Total discount period = 16 + 30 = 46 days Bank discount formula: $$D = M \times d \times \frac{t_d}{360}$$ where - $D$ = bank discount amount - $d$ = discount rate (8% = 0.08) - $t_d$ = discount period (46 days) 5. **Step 4: Calculate proceeds (P) received by Amy.** Proceeds = Maturity value - Bank discount $$P = M - D = M - M \times d \times \frac{t_d}{360} = M \left(1 - d \times \frac{t_d}{360}\right)$$ Given $P = 15392.54$, substitute values: $$15392.54 = M \left(1 - 0.08 \times \frac{46}{360}\right)$$ Calculate the factor: $$1 - 0.08 \times \frac{46}{360} = 1 - 0.08 \times 0.1278 = 1 - 0.01022 = 0.98978$$ So, $$M = \frac{15392.54}{0.98978} = 15556.20$$ 6. **Step 5: Calculate face value $F$.** Recall maturity value formula: $$M = F \times \left(1 + 0.10 \times \frac{120}{360}\right) = F \times (1 + 0.10 \times 0.3333) = F \times 1.0333$$ So, $$F = \frac{M}{1.0333} = \frac{15556.20}{1.0333} = 15050.00$$ 7. **Step 6: Calculate bank discount amount $D$.** $$D = M \times 0.08 \times \frac{46}{360} = 15556.20 \times 0.08 \times 0.1278 = 159.66$$ 8. **Step 7: Calculate interest Amy receives.** Interest = Maturity value - Face value $$\text{Interest} = 15556.20 - 15050.00 = 506.20$$ **Final answers:** i. Maturity date = 1 July 2025 ii. Maturity value = 15556.20 iii. Bank discount amount = 159.66 iv. Face value = 15050.00 v. Interest Amy receives = 506.20