Questions: What is the purchase price of a 50-day T-bill with a maturity value of 1,522 that earns an annual interest rate of 5.611%? (Assume a 360-day year.) The purchase price is (Round to two decimal places.)

Solution Steps

To find the purchase price of a 50-day T-bill with a maturity value of $1,522 and an annual interest rate of 5.611%, we can use the formula for the purchase price of a T-bill:

\[ \text{Purchase Price} = \text{Maturity Value} \times \left(1 - \frac{\text{Interest Rate} \times \text{Days to Maturity}}{360}\right) \]

Where:

• Maturity Value = $1,522
• Interest Rate = 5.611% (expressed as a decimal)
• Days to Maturity = 50

We are given the following values:

• Maturity Value: \( MV = 1522 \)
• Annual Interest Rate: \( r = 5.611\% = 0.05611 \)
• Days to Maturity: \( t = 50 \)
• Days in Year: \( D = 360 \)

The formula for the purchase price \( P \) of a T-bill is given by:

\[ P = MV \times \left(1 - \frac{r \times t}{D}\right) \]

Substituting the known values into the formula:

\[ P = 1522 \times \left(1 - \frac{0.05611 \times 50}{360}\right) \]

First, calculate the interest component:

\[ \frac{0.05611 \times 50}{360} = \frac{2.8055}{360} \approx 0.0078 \]

Now substitute back into the formula:

\[ P = 1522 \times (1 - 0.0078) = 1522 \times 0.9922 \approx 1510.14 \]

Final Answer