Determine the fair value of a treasury bill that has a yield of 5.67% p.a. and a maturity of 180 days The face value of the bill is $100.00, and uses a 360-day basis for calculating interest. (Please round your answer to two decimal places)
Question
Determine the fair value of a treasury bill that has a yield of 5.67% p.a. and a maturity of 180 days The face value of the bill is $100.00, and uses a 360-day basis for calculating interest. (Please round your answer to two decimal places)
Solution 1
To calculate the fair value of a treasury bill, we use the formula:
Fair Value = Face Value / (1 + (Yield * (Days to Maturity / 360)))
Given that the face value is $100, the yield is 5.67% (or 0.0567 when expressed as a decimal), and the days to maturity is 180, we can substitute these values into the formula:
Fair Value = $100 / (1 + (0.0567 * (180 / 360)))
This simplifies to:
Fair Value = $100 / (1 + (0.0567 * 0.5))
Fair Value = $100 / (1 + 0.02835)
Fair Value = $100 / 1.02835
After performing the division, we find that the fair value of the treasury bill is approximately $97.24.
Solution 2
To calculate the fair value of a treasury bill, we use the formula:
Fair Value = Face Value / (1 + (Yield * (Days to Maturity / 360)))
Given in the problem:
Face Value = $100 Yield = 5.67% = 0.0567 (in decimal form) Days to Maturity = 180 days
Substituting these values into the formula:
Fair Value = $100 / (1 + (0.0567 * (180 / 360)))
Solving the equation:
Fair Value = 100 / (1 + 0.02835) Fair Value = $100 / 1.02835
Finally, rounding to two decimal places, the fair value of the treasury bill is approximately $97.24.
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