https://file.aiquickdraw.com/mathbot/file/1730669494092wfe5ksf5.jpg

The purchase price is ​$ ​(Round to two decimal​ places.)

To calculate the purchase price of the T-bill, we use the following formula for discount pricing on Treasury bills:

\[
\text{Purchase Price} = \text{Maturity Value} \times \left(1 - \frac{\text{Interest Rate} \times \text{Days to Maturity}}{360}\right)
\]

where:
- **Maturity Value** is given as $1,846.
- **Annual Interest Rate** is 3.989% (or 0.03989 in decimal form).
- **Days to Maturity** is 50 days.
- **360-day year** assumption.

### Step-by-Step Calculation

1. Convert the interest rate to decimal form:
   \[
   \text{Interest Rate} = 0.03989
   \]

2. Calculate the term for the interest:
   \[
   \frac{0.03989 \times 50}{360} = 0.0055404167
   \]

3. Calculate the purchase price:
   \[
   \text{Purchase Price} = 1846 \times (1 - 0.0055404167)
   \]
   \[
   \text{Purchase Price} = 1846 \times 0.9944595833
   \]
   \[
   \text{Purchase Price} \approx 1835.52
   \]

### Final Answer
The purchase price of the T-bill is approximately **$1835.52**.

Would you like further clarification or additional details?

---

Here are some related questions for further understanding:
1. What is the formula to calculate the interest on Treasury bills?
2. Why is a 360-day year used in financial calculations instead of a 365-day year?
3. How does the purchase price change if the interest rate increases?
4. How is the yield on a Treasury bill calculated given its purchase price?
5. What are some other short-term financial instruments similar to Treasury bills?

**Tip:** Remember, T-bills are usually sold at a discount, meaning their purchase price is less than the maturity value.

What is the purchase price of a 50-day T-bill with a maturity value of $1,846 that earns an annual interest rate of 3.989%? (Assume a 360-day year.)

Find the purchase price of a 50-day Treasury bill with a maturity value of $1,846 and an annual interest rate of 3.989%, using a 360-day year. Learn about discount pricing and the formula for calculating T-bill purchase prices.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation