Please help?
The Treasury Department auctioned $21 billion in 3-month bills in denominations of $10,000 at a discount rate of 4.965%.
What would be the effective rate of interest? (Use calendar year. Do not round intermediate calculations. Round your answer to the nearest hundredth percent.)
To calculate the effective rate of interest, we need to first understand how discount rates work.
In the case of Treasury bills, the discount rate represents the difference between the purchase price and the face value of the bill. The actual interest earned is the difference between the face value and the purchase price.
Here's how to calculate the effective rate of interest:
1. Calculate the purchase price: The purchase price can be calculated by subtracting the discount amount from the face value. In this case, the face value is $10,000, and the discount rate is 4.965%.
Discount amount = Face value * Discount rate = $10,000 * 0.04965 = $496.50
Purchase price = Face value - Discount amount = $10,000 - $496.50 = $9,503.50
2. Calculate the interest amount: The interest amount earned is the difference between the face value and the purchase price.
Interest amount = Face value - Purchase price = $10,000 - $9,503.50 = $496.50
3. Calculate the effective rate of interest: To calculate the effective rate of interest, divide the interest amount by the purchase price and multiply by 100 to get the percentage.
Effective rate of interest = (Interest amount / Purchase price) * 100
= ($496.50 / $9,503.50) * 100
= 5.22%
Therefore, the effective rate of interest on the Treasury bill is 5.22% (rounded to the nearest hundredth percent).