Question

Assume that 3-month treasury bills totaling $16 billion were sold in $10,000 denominations at a discount rate of 4.200%. in addition, the treasury department sold 6-month bills totaling $14 billion at a discount rate of 4.145%. a. what is the discount amount for 3-month bills?

Answer 1

To find the discount amount for the 3-month bills, you can use the formula:

\[ \text{Discount} = \text{Face Value} \times \text{Discount Rate} \times \left( \frac{\text{Time to Maturity}}{\text{Number of Periods in a Year}} \right) \]

In this case, the face value is $10,000, the discount rate is 4.200%, and the time to maturity is 3 months (or 0.25 years).

\[ \text{Discount} = 10,000 \times 0.042 \times \left( \frac{0.25}{1} \right) \]

\[ \text{Discount} = 10,000 \times 0.0105 = 105 \]

Therefore, the discount amount for the 3-month bills is $105.

Answer 2

The discount amount for 3-month Treasury bills is determined by subtracting the present value of the bill from its face value. The present value is calculated using the discount rate adjusted to the bill's time to maturity. The total discount amount for all the T-bills is the discount per T-bill multiplied by the number of T-bills sold.

Step-by-step explanation:

The student's question involves calculating the discount amount for 3-month Treasury bills. To find the discount amount, you can use the formula for the present value of a discounted bond, given by the formula:

Discount Amount = Face Value - Present Value

The present value is the money you pay today to buy the bill, which will be worth its face value at maturity. Here, the face value is $10,000 (denomination of one T-bill), and the discount rate is 4.200%. Since these are 3-month T-bills, we need to adjust the annual discount rate to a quarterly one.

First, we calculate the present value:

Present Value = Face Value / (1 + (Discount Rate x (Days to Maturity/360)))

Let's substitute the known values into the formula:

Present Value = $10,000 / (1 + (0.042 x (90/360)))

Solving the above, we get the present value. Then, the discount amount is $10,000 minus the present value. This gives us the discount amount for each T-bill. To get the total discount amount for all $16 billion worth of T-bills, we multiply the discount per T-bill by the total number of T-bills sold (which is $16 billion divided by the denomination of each T-bill).