What is the purchase price of a​ 50-day T-bill with a maturity value of

​$1 comma 1011,101

that earns an annual interest rate of

6.1466.146​%?

​(Assume a​ 360-day year.)

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Part 1

The purchase price is

​$enter your response here.

To determine the purchase price of a 50-day T-bill, we can use the following formula for calculating the purchase price:

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

Where:
- $ r $ is the annual interest rate (as a decimal),
- $ t $ is the time period of the T-bill (in days),
- The maturity value is the final value paid at maturity.

### Given:
- Maturity value = $ 1,101 $
- Annual interest rate $ r = 6.146\% = 0.06146 $
- Time $ t = 50 $ days
- $ 360 $-day year assumption

### Step-by-Step Calculation:

1. **Interest rate component:**
   \[
   \frac{r \times t}{360} = \frac{0.06146 \times 50}{360} = 0.008535
   \]

2. **Purchase Price formula:**
   \[
   \text{Purchase Price} = 1,101 \times (1 - 0.008535)
   \]
   \[
   \text{Purchase Price} = 1,101 \times 0.991465
   \]
   \[
   \text{Purchase Price} = 1,091.10
   \]

### Final Answer:
The purchase price is **$1,091.10**.

Would you like further clarification or more details on the calculation?

### Related Questions:
1. How is the interest rate component calculated in T-bill pricing?
2. What is the significance of using a 360-day year in such calculations?
3. How does the time period affect the purchase price of T-bills?
4. What is the difference between the purchase price and the maturity value?
5. How would a change in the interest rate affect the purchase price?

### Tip:
Always convert the interest rate into decimal form before using it in formulas.

What is the purchase price of a 50-day T-bill with a maturity value of $1,101 that earns an annual interest rate of 6.146%? (Assume a 360-day year.)

Learn how to calculate the purchase price of a 50-day Treasury bill with a maturity value of $1,101 and an annual interest rate of 6.146%. This guide explains the T-bill pricing formula, step-by-step solution, and key finance concepts. Suitable for advanced high school or college finance students.

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