Question

Suppose you purchase a T-bill that is 103 days from maturity for $9,770. The T-bill has a face value of $10,000.

a. Calculate the T-bill’s quoted discount yield.
b. Calculate the T-bill’s bond equivalent yield.

Answer 1

Solution:

When the No. of days in a year is taken as 365

Quoted Discount yield = 8.15 %

Bond Equivalent Yield = 8.34 %

When the No. of days in a year is taken as 360

Quoted Discount yield = 8.04 %

Bond Equivalent Yield = 8.23 %

Please find the detailed calculations of the above solution as follows:

a. Calculation of the T-bill’s quoted discount yield:           

The formula for calculation of discount yield of a T-Bill when the No. of days in a year = 365

= [ (Face value – Purchase Price)/ Face value ] * ( 365 / No. of days to maturity )

As per the Information given in the question we have

Face Value = $ 10,000   ; Purchase Price = $ 9,770    ; No. of days to maturity = 103

Applying the above values in the formula we have

= [ ( 10000 – 9770 ) / 10000 ] * ( 365/103 )

= ( 230/10000) * 3.5437

= 0.0230 * 3.4537

= 0.0815 = 8.15 %

The formula for calculation of discount yield of a T-Bill when the No. of days in a year = 360

= [ (Face value – Purchase Price)/ Face value ] * ( 360 / No. of days to maturity )

As per the Information given in the question we have

Face Value = $ 10,000   ; Purchase Price = $ 9,770    ; No. of days to maturity = 103

Applying the above values in the formula we have

= [ ( 10000 – 9770 ) / 10000 ] * ( 360/103 )

= ( 230/10000) * 3.4951

= 0.0230 * 3.4951

= 0.0804 = 8.04 %

b. Calculation of the T-bill’s Bond Equivalent yield:           

The formula for calculation of Bond equivalent yield of a T-Bill when the No. of days in a year = 365

= [ (Face value – Purchase Price)/ Purchase Price ] * ( 365 / No. of days to Maturity)

As per the Information given in the question we have

Face Value = $ 10,000   ; Purchase Price = $ 9,770    ; No. of days to maturity = 103

Applying the above values in the formula we have

= [ ( 10000 – 9770 ) / 9770 ] * ( 365/103 )

=( 230 / 9770 ) * 3.5437

= 0.0235 * 3.5437

= 0.0834 = 8.34 %

The formula for calculation of Bond equivalent yield of a T-Bill when the No. of days in a year = 360

= [ (Face value – Purchase Price)/ Purchase Price ] * ( 360 / No. of days to Maturity)

As per the Information given in the question we have

Face Value = $ 10,000   ; Purchase Price = $ 9,770    ; No. of days to maturity = 103

Applying the above values in the formula we have

= [ ( 10000 – 9770 ) / 9770 ] * ( 360/103 )

=( 230 / 9770 ) * 3.4951

= 0.0235 * 3.4951

= 0.0823 = 8.23 %