A $10,000 T-bill matures on 10/31/24. I bought it on 6/18/24. The simple discount
rate was 1.26%. How much did I pay for it? use 365 days

To calculate the price paid for the T-bill, we use the formula for the purchase price based on the simple discount rate:

\[
\text{Purchase Price} = \text{Maturity Value} \times \left(1 - \left(\frac{d \times t}{360}\right)\right)
\]

where:
- $ d $ is the discount rate (1.26% or 0.0126),
- $ t $ is the time to maturity in days,
- $ \text{Maturity Value} $ is the face value of the T-bill ($10,000).

### Step 1: Calculate the time to maturity (days between 6/18/24 and 10/31/24)
- From June 18, 2024, to October 31, 2024, let's calculate the number of days.

\[
t = \text{Days between 6/18/24 and 10/31/24}
\]

Now I'll calculate the exact number of days and use this to find the price.The time to maturity is 135 days.

### Step 2: Use the simple discount formula
We now apply the discount formula:

\[
\text{Purchase Price} = 10,000 \times \left(1 - \left(\frac{0.0126 \times 135}{365}\right)\right)
\]

Now, let's calculate the purchase price.The purchase price of the T-bill is approximately **$9,953.40**.

Would you like any additional details or have questions on this calculation?

Here are 5 related questions:
1. What is the significance of the discount rate in T-bill pricing?
2. How would the price change if the discount rate were higher?
3. What is the difference between simple and compound interest in bond pricing?
4. How does the number of days to maturity affect the purchase price?
5. Can you explain the relationship between the purchase price and the maturity value?

**Tip:** When buying T-bills, remember that the discount rate directly impacts the return on investment—the lower the purchase price, the higher the potential gain at maturity.

A $10,000 T-bill matures on 10/31/24. I bought it on 6/18/24. The simple discount rate was 1.26%. How much did I pay for it? Use 365 days.

Learn how to calculate the purchase price of a $10,000 T-bill maturing on 10/31/24, bought on 6/18/24, with a simple discount rate of 1.26%. Understand the key formula for simple discount calculations and how the number of days to maturity impacts the price. Suitable for advanced high school or college-level finance and math students.

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