If you purchase $24,000 in U.S. Treasury Bills with a discount rate of 4.7% for a period of 26 weeks, what is the effective interest rate (as a %)? Round to the nearest hundredth percent.
 
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To calculate the effective interest rate for a U.S. Treasury Bill purchase, we can use the following formula for a T-bill's interest rate:

\[
\text{Effective Interest Rate} = \frac{\text{Discount}}{\text{Purchase Price}} \times \frac{365}{n}
\]

Where:
- Discount = $\text{Face Value} - \text{Purchase Price}$
- $ n $ = Number of days the bill is held (in this case, $ 26 $ weeks = $ 26 \times 7 = 182 $ days)

Given:
- Face Value = $24,000
- Discount Rate = 4.7%
- $ n = 182 $ days

### Step 1: Calculate the Purchase Price
The purchase price is calculated by reducing the face value by the discount rate:

\[
\text{Purchase Price} = \text{Face Value} \times \left( 1 - \frac{\text{Discount Rate}}{100} \right)
\]

\[
\text{Purchase Price} = 24000 \times \left( 1 - \frac{4.7}{100} \right)
\]

\[
\text{Purchase Price} = 24000 \times 0.953 = 22872
\]

### Step 2: Calculate the Discount
\[
\text{Discount} = \text{Face Value} - \text{Purchase Price} = 24000 - 22872 = 1128
\]

### Step 3: Calculate the Effective Interest Rate
\[
\text{Effective Interest Rate} = \frac{1128}{22872} \times \frac{365}{182}
\]

Let's calculate this value.

The effective interest rate for purchasing $24,000 in U.S. Treasury Bills with a discount rate of 4.7% over a period of 26 weeks is **9.89%**.

Would you like further clarification or details on any step?

Here are 5 related questions to deepen your understanding:
1. How does the effective interest rate change if the holding period increases?
2. What would be the impact if the discount rate were 5% instead of 4.7%?
3. How is the nominal interest rate different from the effective interest rate?
4. Can you calculate the interest earned if the Treasury Bill was held for only 13 weeks?
5. How do Treasury Bills compare with Treasury Bonds in terms of interest rate calculations?

**Tip:** The effective interest rate is usually higher than the nominal rate due to compounding over the year.

If you purchase $24,000 in U.S. Treasury Bills with a discount rate of 4.7% for a period of 26 weeks, what is the effective interest rate (as a %)? Round to the nearest hundredth percent.

Learn how to calculate the effective interest rate for purchasing $24,000 in U.S. Treasury Bills with a 4.7% discount rate for a 26-week period. This detailed solution covers key financial concepts, including discount and interest rate formulas, and is suitable for college-level finance students.

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