1. **State the problem:** Calculate the discount period for a loan made on January 9 with a face value of 3500, a simple interest rate of 9%, discounted at 9 March. 2. **Formula and explanation:** The discount period is the number of days from the discount date to the maturity date. Here, the maturity date is 120 days from January 9. 3. **Calculate the discount period:** - Days in January after 9th: $31 - 9 = 22$ - Days in February: $28$ - Days in March before 9th: $9 - 5 = 4$ (assuming discount date is March 5) - Total discount period: $22 + 28 + 4 = 54$ days 4. **Answer:** The discount period is 54 days. --- 1. **State the problem:** Calculate the discount amount $B$ for the loan. 2. **Formula:** $B = m \times r \times \frac{T}{360}$ where $m=3500$, $r=9\% = 0.09$, $T=54$ days. 3. **Calculation:** $$B = 3500 \times 0.09 \times \frac{54}{360} = 3500 \times 0.09 \times 0.15 = 47.25$$ 4. **Answer:** The discount is $47.25$. --- 1. **State the problem:** Calculate the proceeds $P$ from the loan. 2. **Formula:** $P = m - B$ where $m=3500$ and $B=47.25$. 3. **Calculation:** $$P = 3500 - 47.25 = 3452.75$$ 4. **Answer:** The proceeds are $3452.75$. --- 1. **State the problem:** Find the effective simple interest rate corresponding to a discount rate of 8% for 120 days. 2. **Formula:** Effective rate $r_e = \frac{d}{1 - d \times \frac{T}{360}}$ where $d=0.08$, $T=120$. 3. **Calculation:** $$r_e = \frac{0.08}{1 - 0.08 \times \frac{120}{360}} = \frac{0.08}{1 - 0.08 \times 0.3333} = \frac{0.08}{1 - 0.0267} = \frac{0.08}{0.9733} \approx 0.0821 = 8.21\%$$ 4. **Answer:** The effective simple interest rate is approximately 8.21%.