The Treasury Department auctioned $21 billion in three month bills in denominations of ten thousand dollars at a discount rate of 4.965%. What would be the effective rate of interest?
To find the effective rate of interest, we need to convert the discount rate to an effective annual rate. The discount rate is a percentage of the face value of the bill that investors pay to purchase it. In this case, the discount rate is 4.965%.
To calculate the effective rate of interest, we can use the formula:
Effective Rate = (Discount / Face Value) * (360 / Days)
Here's how we can apply the formula to the given information:
- Let's assume the face value of the bill is $10,000.
- The discount is 4.965% of the face value, which is (4.965 / 100) * $10,000 = $496.50.
- The bill is a three-month bill, which means there are 91 days until maturity.
- We use 360 days in the denominator as it is typically used to calculate the effective rate for Treasury bills.
Using the formula, we can calculate the effective rate of interest:
Effective Rate = ($496.50 / $10,000) * (360 / 91)
Simplifying the expression:
Effective Rate = 0.04965 * 3.956
Calculating the value:
Effective Rate ≈ 0.1965
Therefore, the effective rate of interest for this three-month bill is approximately 19.65%.