if you purchase $28,000 in U.S. Treasury Bills with a discount rate of 4.1% for a period of 26 weeks, what is the effective interest rate (as a %)? Round to the nearest hundredth percent.

To determine the effective interest rate for the U.S. Treasury Bills given the provided details, follow these steps:

1. **Determine the purchase price and the face value:**
   \[
   P = \$28,000 \quad (\text{purchase price})
   \]
   \[
   \text{Discount Rate} = 4.1\% = 0.041
   \]
   \[
   \text{Period} = 26 \text{ weeks} = 26 \times 7 = 182 \text{ days}
   \]

2. **Calculate the face value (F) of the Treasury Bill:**
   \[
   F = \frac{P}{1 - (\text{Discount Rate} \times \frac{\text{Days to Maturity}}{360})}
   \]
   Substituting the values:
   \[
   F = \frac{28,000}{1 - (0.041 \times \frac{182}{360})}
   \]
   \[
   F = \frac{28,000}{1 - (0.041 \times 0.5056)}
   \]
   \[
   F = \frac{28,000}{1 - 0.020728}
   \]
   \[
   F = \frac{28,000}{0.979272} \approx 28,600.86
   \]

3. **Calculate the effective interest rate (EIR):**
   \[
   \text{EIR} = \left( \frac{F - P}{P} \right) \times \frac{365}{\text{Days to Maturity}}
   \]
   \[
   \text{EIR} = \left( \frac{28,600.86 - 28,000}{28,000} \right) \times \frac{365}{182}
   \]
   \[
   \text{EIR} = \left( \frac{600.86}{28,000} \right) \times 2.0055
   \]
   \[
   \text{EIR} = 0.021459 \times 2.0055 \approx 0.04303
   \]

4. **Convert to a percentage and round to the nearest hundredth percent:**
   \[
   \text{EIR} \approx 4.30\%
   \]

Thus, the effective interest rate, rounded to the nearest hundredth percent, is approximately **4.30%**.

Would you like any more details or have any questions?

Here are five questions you might ask next:
1. How do you calculate the yield of a bond?
2. What is the difference between nominal and effective interest rates?
3. How do you determine the maturity value of a zero-coupon bond?
4. What are the tax implications of investing in U.S. Treasury Bills?
5. How do changes in interest rates affect bond prices?

**Tip:** When calculating financial metrics, always ensure your time periods are consistent (e.g., converting weeks to days) to maintain accuracy in your results.

Learn how to calculate the effective interest rate of U.S. Treasury Bills purchased at $28,000 with a discount rate of 4.1% for a period of 26 weeks. Follow a detailed step-by-step solution covering finance concepts, including effective interest rate calculation formulas. Suitable for undergraduate students studying finance and economics.

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