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.