What would be the purchase price for a 180 day, $100,000 U.S. Treasury bill sold at a 4.25% discount rate

To find the purchase price of a 180-day U.S. Treasury bill with a face value of $100,000 and a discount rate of 4.25%, we can use the formula for calculating the price of a T-bill sold at a discount:

\[
\text{Price} = \text{Face Value} \times \left(1 - \frac{\text{Discount Rate} \times \text{Days}}{360}\right)
\]

Inserting the values:

- **Face Value** = $100,000
- **Discount Rate** = 4.25% = 0.0425
- **Days** = 180

### Calculation:
\[
\text{Price} = 100,000 \times \left(1 - \frac{0.0425 \times 180}{360}\right)
\]

#### Step-by-Step Calculation:
1. Calculate the fraction of the year for the discount rate:  
   $\frac{180}{360} = 0.5$

2. Apply this to the discount rate:
   $0.0425 \times 0.5 = 0.02125$

3. Subtract this value from 1:
   $1 - 0.02125 = 0.97875$

4. Multiply by the face value:
   \[
   \text{Price} = 100,000 \times 0.97875 = 97,875
   \]

### Answer:
The purchase price for the 180-day, $100,000 U.S. Treasury bill sold at a 4.25% discount rate is **$97,875**.

Would you like more details on this calculation or have any questions?

Here are some related questions:
1. How would the purchase price change with different discount rates?
2. What is the formula for calculating the purchase price of a T-bill with different days to maturity?
3. How does the discount rate affect the yield of a T-bill?
4. How would the calculation differ if the interest was compounded?
5. What is the effective yield for this T-bill?

**Tip:** Treasury bills are typically quoted on a discount basis, so understanding the discount rate helps you determine the purchase price without needing to calculate compound interest.

Learn how to calculate the purchase price of a 180-day, $100,000 U.S. Treasury bill with a 4.25% discount rate using the discount formula. This step-by-step solution demonstrates the financial concept of discounting and its applications in calculating T-bill prices. Suitable for high school students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation