A 90-day bank bill that promises to pay $1 million at its maturity was issued 44 days ago. Calculate its price today if it is traded at a simple interest yield of 3.0% p.a. (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)
Question
A 90-day bank bill that promises to pay $1 million at its maturity was issued 44 days ago. Calculate its price today if it is traded at a simple interest yield of 3.0% p.a. (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)
Solution
To calculate the price of the bank bill, we need to discount its face value by the remaining time to maturity and the yield.
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First, we need to calculate the remaining time to maturity. The bank bill has a maturity of 90 days and it was issued 44 days ago, so there are 90 - 44 = 46 days left until maturity.
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The yield is given as a simple annual interest rate, so we need to convert it to a daily rate by dividing by the number of days in a year. Assuming a year has 365 days, the daily yield is 3.0% / 365 = 0.00821917808%.
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Now we can calculate the price of the bank bill. This is the face value divided by 1 plus the yield times the remaining time to maturity.
So, the price is 999,280.58
Therefore, the price of the bank bill today is $999,280.58.
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