(a) To buy a Treasury bill (T-bill) that matures to $10,000 in 6 months, you must pay $9700. What annual simple interest rate does this earn? (Round your answer to one decimal place.)
 %

(b) If the bank charges a fee of $40 to buy a T-bill, what is the actual interest rate you earn? (Round your answer to one decimal place.)
 %

To solve these questions, let's break down each part.

### Part (a) - Finding the Annual Simple Interest Rate

Given:
- The future value of the T-bill is $10,000.
- The present value (or the price you pay now) is $9,700.
- The time until maturity is 6 months, which is $ \frac{1}{2} $ year.

To calculate the annual simple interest rate, we use the formula:

\[
\text{Interest Rate (r)} = \frac{\text{Interest}}{\text{Principal} \times \text{Time}}
\]

First, calculate the interest earned:

\[
\text{Interest} = \text{Future Value} - \text{Principal} = 10,000 - 9,700 = 300
\]

Now, apply the formula for the interest rate. The time is 0.5 years:

\[
r = \frac{300}{9,700 \times 0.5}
\]

Let's compute this.The annual simple interest rate for the T-bill is approximately **6.2%**.

### Part (b) - Finding the Actual Interest Rate (Including the Fee)

If the bank charges a fee of $40 to buy the T-bill, the total cost becomes:

\[
\text{Total Cost} = 9,700 + 40 = 9,740
\]

Now, we need to calculate the actual interest rate earned based on this new principal of $9,740. We still use the same interest of $300 and time of 0.5 years. The formula remains:

\[
r = \frac{300}{9,740 \times 0.5}
\]

Let's compute the new interest rate.The actual annual simple interest rate, considering the $40 fee, is approximately **6.2%**.

### Summary:
- **(a)** The annual simple interest rate without the fee is **6.2%**.
- **(b)** The actual annual interest rate after accounting for the fee is **6.2%**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does compound interest differ from simple interest in similar scenarios?
2. What would happen to the interest rate if the maturity period was 1 year?
3. How does the purchase of a T-bill compare to other short-term investments?
4. How would a larger fee affect the actual interest rate?
5. What are other ways to calculate the yield on T-bills?

**Tip:** Always consider transaction fees when evaluating the true return on investment.

To buy a Treasury bill (T-bill) that matures to $10,000 in 6 months, you must pay $9700. What annual simple interest rate does this earn? If the bank charges a fee of $40 to buy a T-bill, what is the actual interest rate you earn?

Learn how to calculate the annual simple interest rate for a Treasury bill (T-bill) investment maturing to $10,000 in 6 months. This problem covers key financial concepts such as simple interest, interest rate calculation, and the impact of fees on actual interest rates. Suitable for students in Grades 9-12.

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