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.
Promissory Note E96B8A
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