Question: When preparing for a business trip to China, Kaylee Putbrese determined she needed to bring $6,500. How much must she borrow for a simple discount note at 5% for 45 days? Note: Use 360 days a year. Round your answer to the nearest cent.
1. **State the problem:** Kaylee needs $6500 for her trip and wants to borrow this amount using a simple discount note at 5% annual interest for 45 days.
2. **Formula for simple discount note:** The amount borrowed (principal) $P$ is related to the maturity value $M$ by the formula:
$$P = M - D$$
where $D$ is the discount.
The discount $D$ is calculated as:
$$D = M \times r \times \frac{t}{360}$$
where $r$ is the annual interest rate and $t$ is the time in days.
3. **Identify values:**
- Maturity value needed $M = 6500$
- Annual interest rate $r = 0.05$
- Time $t = 45$ days
4. **Calculate the discount:**
$$D = 6500 \times 0.05 \times \frac{45}{360}$$
$$D = 6500 \times 0.05 \times 0.125$$
$$D = 6500 \times 0.00625 = 40.625$$
5. **Calculate the amount to borrow:**
$$P = 6500 - 40.625 = 6459.375$$
6. **Round to nearest cent:**
$$P = 6459.38$$
**Answer:** Kaylee must borrow $6459.38$ for the simple discount note.