You pay \$9,850 for a 180-day Treasury bill (T-bill) with a face value of \$10,000. What is the annualized discount rate (using a 360-day year) for this T-bill?

• A. 3.00\%
• B. 2.96\%
• C. 2.50\%
• D. 3.06\%

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the problem. The goal is to calculate the annualized discount rate for a Treasury bill (T-bill) using a 360-day year. The discount rate is based on the difference between the face value and the purchase price, annualized to reflect a full year.
2. Step 2: Calculate the discount amount. The discount amount is the difference between the face value and the purchase price of the T-bill. Use the formula: Discount Amount = Face Value - Purchase Price. In this case, the face value is \$10,000 and the purchase price is \$9,850.
3. Step 3: Determine the discount rate for the 180-day period. The formula for the discount rate is: Discount Rate = (Discount Amount / Face Value) × 100. This gives the percentage discount for the 180-day period.
4. Step 4: Annualize the discount rate. Since the T-bill is for 180 days and the year is considered to have 360 days, the annualized discount rate is calculated by multiplying the 180-day discount rate by (360 / 180). The formula is: Annualized Discount Rate = Discount Rate × (360 / 180).
5. Step 5: Compare the calculated annualized discount rate to the given options (3.00%, 2.96%, 2.50%, and 3.06%) to identify the correct answer.