Final answer:
The money market yield is calculated as 5.3437%, the bond equivalent yield is 5.4188%, and the discount rate at which the Treasury bill was offered is 1.3333%. These calculations assist in evaluating the returns on Treasury bill investments.
Step-by-step explanation:
Calculating Treasury Bill Yields and Discount Rates
To address the student's question regarding Treasury bills, we need to calculate the money market yield, the bond equivalent yield, and the discount rate at which the Treasury bill was offered. Given that a 3-month Treasury bill was sold at a price of $148,000 and had a face value of $150,000, the calculations are as follows:
Money Market Yield: The money market yield (MMY) can be calculated using the formula MMY = [(Face Value - Purchase Price)/Purchase Price] * (360/Days to Maturity). In this case, MMY = [($150,000 - $148,000)/$148,000] * (360/91) = 0.013514 * 3.956044 = 5.3437%, approximately.
Bond Equivalent Yield: The bond equivalent yield (BEY) is calculated differently, as it annualizes the yield based on a 365-day year and is given by BEY = [(Face Value - Purchase Price)/Purchase Price] * (365/Days to Maturity). For the given Treasury bill, BEY = [($150,000 - $148,000)/$148,000] * (365/91) = 0.013514 * 4.010989 = 5.4188%, approximately.
Discount Rate: The discount rate is found by calculating the discount amount as a percentage of the face value, using the formula Discount Rate = (Face Value - Purchase Price)/Face Value. Therefore, Discount Rate = ($150,000 - $148,000)/$150,000 = $2,000/$150,000 = 0.013333 or 1.3333%.
Remember that the money market yield is based on a 360-day year which is standard for the U.S. money market, whereas the bond equivalent yield is based on the actual number of days in the year. Understanding these yields and rates can be beneficial for assessing investment opportunities.