Let's break down the solution step-by-step: ### **Given Data** | | 3-Month T-Bill | 6-Month T-Bill | |-------------------|:--------------:|:--------------:| | Face Value | $10,000.00 | $10,000.00 | | Price at Sale | $9,993.86 | $9,976.85 | | Discount | $6.14 | $23.15 | ### **Step 1: Calculate the Simple Yield (Holding Period Yield)** The formula for the simple yield (holding period yield) is: \[ \text{Simple Yield} = \frac{\text{Discount}}{\text{Price at Sale}} \] #### **For 3-Month T-Bill:** \[ \text{Simple Yield}_{3m} = \frac{6.14}{9,993.86} = 0.0006145 \approx 0.06145\% \] #### **For 6-Month T-Bill:** \[ \text{Simple Yield}_{6m} = \frac{23.15}{9,976.85} = 0.0023219 \approx 0.23219\% \] --- ### **Step 2: Calculate the Annualized Yield** Annualized yield = Simple yield × (12 / months to maturity) #### **For 3-Month T-Bill:** \[ \text{Annualized Yield}_{3m} = 0.0006145 \times \left(\frac{12}{3}\right) = 0.0006145 \times 4 = 0.002458 \approx 0.2458\% \] #### **For 6-Month T-Bill:** \[ \text{Annualized Yield}_{6m} = 0.0023219 \times \left(\frac{12}{6}\right) = 0.0023219 \times 2 = 0.0046438 \approx 0.4644\% \] --- ### **Step 3: Final Answers Summary** | | 3-Month T-Bill | 6-Month T-Bill | |-------------------|:-----------------------:|:-------------------------:| | Simple Yield | 0.06145% | 0.23219% | | Annualized Yield | 0.2458% | 0.4644% | --- ### **Boxed Final Answers** #### **3-Month T-Bill** - **Simple Yield:** 0.06145% - **Annualized Yield:** 0.2458% #### **6-Month T-Bill** - **Simple Yield:** 0.23219% - **Annualized Yield:** 0.4644% --- **Let me know if you need these in a different format or further explanation!**

Certainly! Let's go through the detailed step-by-step calculations for both the 3-month and 6-month Treasury bills, including all formulas, explanations, and final answers. --- ### **Given Data** | Description | 3-Month T-Bill | 6-Month T-Bill | |---------------------------|:--------------:|:--------------:| | Face Value | $10,000.00 | $10,000.00 | | Price at Sale | $9,993.86 | $9,976.85 | | Discount (interest) | $6.14 | $23.15 | --- ### **Part 1: Calculate the Simple Yield (Holding Period Yield)** **Definition:** The simple yield (or holding period yield) measures the return over the period the T-bill is held, calculated as: \[ \text{Simple Yield} = \frac{\text{Discount}}{\text{Price at Sale}} \] **Note:** The discount is the difference between the face value and the purchase price, but since the problem provides the discount directly, we will use it. --- ### **Step 1: Calculate the Simple Yield for each T-Bill** #### **For 3-Month T-Bill:** \[ \text{Simple Yield}_{3m} = \frac{\text{Discount}}{\text{Price at Sale}} = \frac{6.14}{9,993.86} \] Calculate numerator and denominator: \[ \text{Simple Yield}_{3m} = \frac{6.14}{9,993.86} \approx 0.0006145 \] Expressed as a percentage: \[ 0.0006145 \times 100 = 0.06145\% \] --- #### **For 6-Month T-Bill:** \[ \text{Simple Yield}_{6m} = \frac{23.15}{9,976.85} \] Calculate: \[ \text{Simple Yield}_{6m} = \frac{23.15}{9,976.85} \approx 0.0023219 \] Expressed as a percentage: \[ 0.0023219 \times 100 = 0.23219\% \] --- ### **Part 2: Calculate the Annualized Yield** **Definition:** Annualized yield scales the short-term yield to an annual basis assuming the same rate applies over a year. The formula: \[ \text{Annualized Yield} = \text{Simple Yield} \times \frac{12}{\text{months to maturity}} \] --- ### **Step 2: Annualize the yields** #### **For 3-Month T-Bill:** \[ \text{Annualized Yield}_{3m} = 0.0006145 \times \left(\frac{12}{3}\right) = 0.0006145 \times 4 \] Calculate: \[ 0.0006145 \times 4 = 0.002458 \] Express as a percentage: \[ 0.002458 \times 100 = 0.2458\% \] --- #### **For 6-Month T-Bill:** \[ \text{Annualized Yield}_{6m} = 0.0023219 \times \left(\frac{12}{6}\right) = 0.0023219 \times 2 \] Calculate: \[ 0.0023219 \times 2 = 0.0046438 \] Express as a percentage: \[ 0.0046438 \times 100 = 0.4644\% \] --- ### **Final Results** | T-Bill Period | Simple Yield (%) | Annualized Yield (%) | |--------------|:----------------:|:--------------------:| | **3-Month** | **0.06145%** | **0.2458%** | | **6-Month** | **0.23219%** | **0.4644%** | --- ### **Summary** - **3-Month T-Bill:** - Simple Yield = **0.06145%** - Annualized Yield = **0.2458%** - **6-Month T-Bill:** - Simple Yield = **0.23219%** - Annualized Yield = **0.4644%** --- If you require further clarification or calculations, please let me know!

Certainly! Here's a detailed step-by-step calculation without tables: --- **Given Data:** - For the 3-month Treasury bill: - Face value = $10,000 - Price at sale = $9,993.86 - Discount (interest earned) = $6.14 - For the 6-month Treasury bill: - Face value = $10,000 - Price at sale = $9,976.85 - Discount = $23.15 --- ### Step 1: Calculate the simple yield (holding period yield) The simple yield is calculated as the ratio of the discount (interest earned) to the price at sale: **Formula:** Simple Yield = Discount / Price at sale For the 3-month bill: Simple Yield = 6.14 / 9,993.86 ≈ 0.0006145 Expressed as a percentage: 0.0006145 × 100 ≈ 0.06145% For the 6-month bill: Simple Yield = 23.15 / 9,976.85 ≈ 0.0023219 Expressed as a percentage: 0.0023219 × 100 ≈ 0.23219% --- ### Step 2: Calculate the annualized yield Since these yields are over a short period (3 months and 6 months), we annualize them by multiplying by the ratio of 12 months to the number of months to maturity: **Formula:** Annualized Yield = Simple Yield × (12 / months to maturity) For the 3-month bill: Annualized Yield = 0.0006145 × (12 / 3) = 0.0006145 × 4 = 0.002458 Expressed as a percentage: 0.002458 × 100 ≈ 0.2458% For the 6-month bill: Annualized Yield = 0.0023219 × (12 / 6) = 0.0023219 × 2 = 0.0046438 Expressed as a percentage: 0.0046438 × 100 ≈ 0.4644% --- ### **Final answers:** - The 3-month Treasury bill has a simple yield of approximately **0.06145%** and an annualized yield of approximately **0.2458%**. - The 6-month Treasury bill has a simple yield of approximately **0.23219%** and an annualized yield of approximately **0.4644%**. Let me know if you'd like these rounded differently or need further explanation!