Suppose you pay $7850 for a $10000 par Treasury bill maturing in 7 months. What is the effective annual rate of return for this investment? 

To determine the **effective annual rate of return** (EAR) on a Treasury bill, we need to follow these steps:

1. **Calculate the rate of return (simple interest) over the 7-month period:**

\[
\text{Rate of return} = \frac{\text{Par value} - \text{Purchase price}}{\text{Purchase price}}
\]

Given:
- Par value = $10,000
- Purchase price = $7,850

\[
\text{Rate of return} = \frac{10,000 - 7,850}{7,850} = \frac{2,150}{7,850} \approx 0.2739 \text{ or } 27.39\%
\]

2. **Convert this 7-month return to an annualized rate of return** using the formula for the effective annual rate (EAR):

\[
\text{EAR} = \left(1 + \frac{\text{Rate of return}}{\text{Months held}}\right)^{12/\text{Months held}} - 1
\]

In this case, the investment is held for 7 months:

\[
\text{EAR} = \left(1 + 0.2739\right)^{12/7} - 1
\]

Now, let's calculate the EAR.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can still calculate the **Effective Annual Rate (EAR)** using this formula:

\[
EAR = \left(1 + \frac{\text{Rate of return}}{\text{Months held}}\right)^{12/\text{Months held}} - 1
\]

For your case:

1. **Rate of return** = $ \frac{10,000 - 7,850}{7,850} = 0.2739 $ or 27.39%.
2. Plug in this result into the EAR formula:

\[
EAR = \left(1 + 0.2739\right)^{12/7} - 1
\]

If you'd like, I can guide you through this calculation manually or help with any other related questions.

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Would you like more details or have any questions? Here are some related questions you might find interesting:

1. What is the difference between EAR and nominal annual rate?
2. How can Treasury bills be used to minimize investment risk?
3. What are other common ways to calculate returns on bonds?
4. How does compound interest affect long-term investments?
5. What is the difference between par value and market value?

**Tip:** Always consider how the time period of your investment affects your actual returns, as shorter periods require adjustments to compare effectively with annual rates.

Suppose you pay $7850 for a $10000 par Treasury bill maturing in 7 months. What is the effective annual rate of return for this investment?

Learn how to calculate the effective annual rate of return for a $7850 investment in a $10000 par Treasury bill maturing in 7 months. This step-by-step solution covers key financial concepts such as simple interest and the effective annual rate formula. Suitable for high school students or anyone interested in investment math.

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