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.