Subjects finance

Loan Discount

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Loan Discount


1. **State the problem:** Cherry wants to take a loan of amount $X$ with a discount rate of 3.5% for 120 days. The proceeds (amount received after discount) is RM 3,300. We need to find the original loan amount $X$. 2. **Formula used:** The proceeds $P$ in a bank discount loan is given by: $$P = X - D$$ where $D$ is the discount. The discount $D$ is calculated as: $$D = X \times r \times \frac{t}{360}$$ where $r$ is the discount rate (as a decimal), and $t$ is the time in days. 3. **Apply the formula:** Given: $r = 3.5\% = 0.035$ $t = 120$ days $P = 3300$ Substitute $D$ into the proceeds formula: $$P = X - X \times r \times \frac{t}{360} = X \left(1 - r \times \frac{t}{360}\right)$$ 4. **Calculate the factor:** $$1 - 0.035 \times \frac{120}{360} = 1 - 0.035 \times \frac{1}{3} = 1 - 0.0116667 = 0.9883333$$ 5. **Find $X$:** $$3300 = X \times 0.9883333$$ $$X = \frac{3300}{0.9883333} \approx 3338.68$$ **Answer:** The original loan amount $X$ is approximately RM 3338.68.