Subjects finance

Promissory Note E96B8A

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** Siti has a 4-month promissory note of 3000 with 9% annual interest. She discounts it on 15 March 2026 at a 12% discount rate. We need to find the proceeds she receives from the bank. 2. **Calculate the maturity value of the note:** The note is for 4 months, so interest is calculated for 4 months. Interest formula: $$I = P \times r \times t$$ where $P=3000$, $r=0.09$ (9% per annum), and $t=\frac{4}{12}$ years. Calculate interest: $$I = 3000 \times 0.09 \times \frac{4}{12} = 3000 \times 0.09 \times 0.3333 = 90$$ Maturity value (amount to be received at maturity): $$M = P + I = 3000 + 90 = 3090$$ 3. **Calculate the time from discount date to maturity:** The note is dated 1 February 2026 and matures in 4 months, so maturity date is 1 June 2026. Discount date is 15 March 2026. Time from discount date to maturity: From 15 March to 1 June is 2 months and 17 days approximately. For simplicity, count days: - From 15 March to 1 April: 16 days - April: 30 days - May: 31 days Total days = 16 + 30 + 31 = 77 days Convert to years: $$t_d = \frac{77}{360} \approx 0.2139$$ 4. **Calculate the bank discount:** Bank discount formula: $$D = M \times d \times t_d$$ where $d=0.12$ (12% discount rate). Calculate discount: $$D = 3090 \times 0.12 \times 0.2139 = 3090 \times 0.02567 = 79.31$$ 5. **Calculate the proceeds:** Proceeds = Maturity value - Discount $$\text{Proceeds} = 3090 - 79.31 = 3010.69$$ **Final answer:** The proceeds Siti receives from the bank is approximately 3010.69.