Question

What is the discount yield, bond equivalent yield, and effective annual return on a $1 million T-bill that currently sells at 95.375 percent of its face value and is 70 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 answers to 3 decimal places. (e.g., 32.161))

Answer 1

Answer :

Discount Yield = [ ( par value - purchase price ) / par value ] * [ 360 / days to maturity ]

= [ ( 100 - 95.375 ) / 100 ] * [ 360 / 70 ]

= 4.625 / 100 * 5.142857 = 0.23786

Discount Yield = 23.786%

Bond Equivalent Yield = [ ( Par value - Purchase price ) / Purchase price ] * [ 365 / Days to maturity ]

= [ ( 100 - 95.375 ) / 95.375 ] * [ 365 / 70 ]

= 4.625 / 95.375 * 5.2142857

= 0.04849279 * 5.2142857 = 0.25286

Bond Equivalent Yield = 25.286%

Effective annual return = ( 1 + r / n )^n - 1

Where, r is bond equivalent yield and n is number of compounding

= [ 1 + 25.286% / ( 365 / 70 ) ]^365/70 - 1

= 1.28008 - 1 = 0.28008

Effective annual return = 28.008%