T-Bill Yield Calculator
Calculation Results:
' + 'Discount Amount: $' + discountAmount.toFixed(2) + " + 'Discount Rate (Bank Discount Yield): ' + discountRatePercent + '%' + 'Investment Rate (Bond Equivalent Yield): ' + investmentRatePercent + '%'; }Understanding Treasury Bills (T-Bills) and Their Yields
Treasury Bills, commonly known as T-Bills, are short-term debt instruments issued by the U.S. Department of the Treasury. They are considered one of the safest investments because they are backed by the full faith and credit of the U.S. government. T-Bills have maturities of one year or less, typically 4, 8, 13, 17, 26, or 52 weeks.
How T-Bills Work
Unlike bonds that pay periodic interest, T-Bills are sold at a discount from their face value (also known as par value). When the T-Bill matures, the investor receives the full face value. The difference between the purchase price and the face value represents the investor's return.
For example, if you buy a 13-week T-Bill with a face value of $10,000 for $9,900, you pay $9,900 upfront. After 13 weeks, you receive $10,000. Your profit is $100.
Key Terms Explained
- Face Value: The amount the investor will receive when the T-Bill matures. This is the par value.
- Purchase Price: The discounted price at which the investor buys the T-Bill. This is always less than the face value.
- Days to Maturity: The number of days remaining until the T-Bill reaches its maturity date.
- Discount Amount: The difference between the Face Value and the Purchase Price. This is the profit an investor makes.
Understanding T-Bill Yields
There are two primary ways to express the yield of a T-Bill, each serving a different purpose:
1. Discount Rate (Bank Discount Yield)
The Discount Rate is the traditional way T-Bills are quoted in the market. It expresses the return as a percentage of the face value, annualized based on a 360-day year. While widely used for quoting, it can be misleading because it doesn't reflect the actual return on the money invested.
The formula for the Discount Rate is:
Discount Rate = (Discount Amount / Face Value) * (360 / Days to Maturity)
This rate is useful for comparing T-Bills with different maturities but should not be directly compared to yields on other investment types like bonds or savings accounts, which typically use a 365-day year and are based on the actual investment amount.
2. Investment Rate (Bond Equivalent Yield – BEY)
The Investment Rate, also known as the Bond Equivalent Yield (BEY) or Money Market Yield, provides a more accurate representation of the actual return on investment. It expresses the return as a percentage of the purchase price, annualized based on a 365-day year. This makes it comparable to the yields of other money market instruments and bonds.
The formula for the Investment Rate is:
Investment Rate = (Discount Amount / Purchase Price) * (365 / Days to Maturity)
The BEY is generally higher than the Discount Rate because it uses the purchase price (a smaller denominator) and a 365-day year (a larger numerator in the annualization factor).
How to Use the Calculator
Our T-Bill Yield Calculator helps you quickly determine both the Discount Rate and the Investment Rate for a given T-Bill. Simply enter the following details:
- Face Value ($): The amount you will receive at maturity.
- Purchase Price ($): The price you pay for the T-Bill.
- Days to Maturity: The number of days until the T-Bill matures.
Click "Calculate Yields" to see the annualized Discount Rate and Investment Rate, helping you make informed decisions about your short-term investments.
Example Calculation
Let's say you purchase a T-Bill with a Face Value of $10,000 for a Purchase Price of $9,900, and it has 91 Days to Maturity.
- Face Value: $10,000
- Purchase Price: $9,900
- Days to Maturity: 91
Using the formulas:
- Discount Amount: $10,000 – $9,900 = $100
- Discount Rate: ($100 / $10,000) * (360 / 91) = 0.01 * 3.956043956 = 0.03956043956 or approximately 3.956%
- Investment Rate: ($100 / $9,900) * (365 / 91) = 0.01010101 * 4.010989011 = 0.04051504052 or approximately 4.052%
As you can see, the Investment Rate provides a slightly higher and more accurate reflection of your actual return on the money you invested.