
Question 3
A $100,000 face value Treasury bill with 54 days to maturity is selling for $98,999. What is the yield to maturity on this security? Round off to two-digits after the decimal point. State your answer as a percentage rate (if your answer is one point two three percent, input 1.23) Please consider the year as 360 days when calculating the yield

To calculate the yield to maturity (YTM) on a Treasury bill, we can use the following formula:

\[
\text{Yield to Maturity (YTM)} = \left( \frac{\text{Face Value} - \text{Purchase Price}}{\text{Purchase Price}} \right) \times \left( \frac{360}{\text{Days to Maturity}} \right)
\]

Where:
- **Face Value** = $100,000
- **Purchase Price** = $98,999
- **Days to Maturity** = 54

### Step 1: Calculate the difference between the Face Value and Purchase Price
\[
\text{Face Value} - \text{Purchase Price} = 100,000 - 98,999 = 1,001
\]

### Step 2: Divide the difference by the Purchase Price
\[
\frac{1,001}{98,999} \approx 0.01011
\]

### Step 3: Multiply by $\frac{360}{54}$
\[
0.01011 \times \frac{360}{54} = 0.01011 \times 6.6667 \approx 0.0674
\]

### Step 4: Convert to a percentage rate
\[
0.0674 \times 100 = 6.74\%
\]

Thus, the yield to maturity (YTM) is approximately **6.74%**.

Would you like any further details or clarification on the process?

---

**Related Questions:**
1. How would the yield change if the purchase price were $99,500?
2. What is the relationship between yield to maturity and the number of days to maturity?
3. How is the formula different if the bill has 365 days instead of 360 days for a year?
4. How would the yield change if the Treasury bill had 180 days to maturity but sold for the same price?
5. Can you calculate the yield for a different face value, say $200,000, with similar data?

**Tip:** Treasury bills are discounted securities, meaning they are sold below face value, and their yield is derived from the price difference over time.

A $100,000 face value Treasury bill with 54 days to maturity is selling for $98,999. What is the yield to maturity on this security? Round off to two-digits after the decimal point. State your answer as a percentage rate (if your answer is one point two three percent, input 1.23) Please consider the year as 360 days when calculating the yield.

This tutorial explains how to calculate the yield to maturity (YTM) on a $100,000 Treasury bill with 54 days to maturity, sold for $98,999. Learn the step-by-step process using the YTM formula, factoring in a 360-day year for financial calculations. Suitable for undergraduate finance and economics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation