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.