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 in interest?
To calculate the effective rate of interest for Treasury bills, you need to consider the discount rate and the time period of the investment. Here's how you can calculate the effective rate in this scenario:
Step 1: Determine the discount amount
The discount amount is the difference between the face value of the bill and the price paid at the auction. In this case, the face value is $10,000, and the price paid at the auction can be calculated by multiplying the face value by the discount rate (4.965% = 0.04965). So, the discount amount would be:
Discount amount = Face value x Discount rate
Discount amount = $10,000 x 0.04965
Discount amount = $496.50
Step 2: Calculate the net investment
The net investment is the amount the investor pays after subtracting the discount amount from the face value. So, the net investment would be:
Net investment = Face value - Discount amount
Net investment = $10,000 - $496.50
Net investment = $9,503.50
Step 3: Determine the time period
In this case, the time period is three months, which is equivalent to one quarter of a year.
Step 4: Calculate the effective interest rate
To calculate the effective interest rate, you need to use the formula:
Effective rate = (Discount amount / Net investment) x (360 / Time period)
In this case:
Effective rate = ($496.50 / $9,503.50) x (360 / 3)
Effective rate ≈ 0.0522 x 120
Effective rate ≈ 6.25%
Therefore, the effective rate of interest for the $10,000 three-month Treasury bill would be approximately 6.25%.