Question

What is the discount yield, bond equivalent yield, and effective annual return on a $1 million Treasury bill that currently sells at 95.375 percent of its face value and is 65 days from maturity? (Use 360 days for discount yield and 365 days in a year for bond equivalent yield and effective annual return. Do not round intermediate calculations. Round your percentage answers to 3 decimal places.)

Answer 1

To calculate the discount yield, bond equivalent yield, and effective annual return on a Treasury bill, we can use the given formulas. For this specific $1 million Treasury bill with a price of 95.375% and 65 days to maturity, the discount yield is 10.923%, the bond equivalent yield is 12.152%, and the effective annual return is 12.449%.

Step-by-step explanation:

To calculate the discount yield, bond equivalent yield, and effective annual return on a Treasury bill, we first need to understand their definitions and formulas.

The discount yield is a measure of the annualized percentage by which the Treasury bill price discounts from its face value. It is calculated as:

Discount Yield = ((Face Value - Price) / Face Value) x (360 / Days to Maturity)

The bond equivalent yield is the annualized yield on a Treasury bill assuming it has a maturity of one year. It is calculated as:

Bond Equivalent Yield = ((Face Value - Price) / Price) x (365 / Days to Maturity)

The effective annual return is the annualized yield on a Treasury bill, taking into account the compounding effect. It is calculated as:

Effective Annual Return = ((1 + Discount Yield)^(365 / Days to Maturity) - 1) x 100

Let's apply these formulas to the given information:

Discount Yield = ((100 - 95.375) / 100) x (360 / 65) = 10.923%

Bond Equivalent Yield = ((100 - 95.375) / 95.375) x (365 / 65) = 12.152%

Effective Annual Return = ((1 + 0.10923)^(365 / 65) - 1) x 100 = 12.449%