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.
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 %
Suppose you purchase a T-bill that is 103 days from maturity for $9,770. The T-bill has...
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