T-Bill Rate Calculator
Use this calculator to determine the Discount Rate (Bank Discount Yield) and Investment Rate (Bond Equivalent Yield) for a Treasury Bill based on its face value, purchase price, and days to maturity.
Calculation Results:
' + 'Discount Rate (Bank Discount Yield): ' + (discountRate * 100).toFixed(4) + '%' + 'Investment Rate (Bond Equivalent Yield): ' + (investmentRate * 100).toFixed(4) + '%'; } .t-bill-calculator-container { font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; background-color: #f9f9f9; padding: 25px; border-radius: 10px; box-shadow: 0 4px 12px rgba(0, 0, 0, 0.1); max-width: 600px; margin: 20px auto; border: 1px solid #e0e0e0; } .t-bill-calculator-container h2 { color: #2c3e50; text-align: center; margin-bottom: 20px; font-size: 1.8em; } .t-bill-calculator-container p { color: #34495e; line-height: 1.6; margin-bottom: 15px; } .calculator-inputs label { display: block; margin-bottom: 8px; color: #34495e; font-weight: bold; } .calculator-inputs input[type="number"] { width: calc(100% – 22px); padding: 10px; margin-bottom: 15px; border: 1px solid #ccc; border-radius: 5px; box-sizing: border-box; font-size: 1em; } .calculator-inputs button { background-color: #007bff; color: white; padding: 12px 20px; border: none; border-radius: 5px; cursor: pointer; font-size: 1.1em; width: 100%; transition: background-color 0.3s ease; } .calculator-inputs button:hover { background-color: #0056b3; } .calculator-results { margin-top: 25px; padding: 15px; background-color: #e9f7ef; border: 1px solid #d4edda; border-radius: 8px; color: #155724; } .calculator-results h3 { color: #28a745; margin-top: 0; margin-bottom: 10px; font-size: 1.4em; } .calculator-results p { margin-bottom: 8px; font-size: 1.1em; } .calculator-results p strong { color: #004085; }Understanding Treasury Bills (T-Bills) and Their Rates
Treasury Bills, commonly known as T-Bills, are short-term debt obligations issued by the U.S. Department of the Treasury. They are a popular investment choice for individuals and institutions seeking a low-risk, short-term investment. Unlike bonds or notes, T-Bills do not pay periodic interest payments (coupons). Instead, they are sold at a discount from their face value (also known as par value), and the investor receives the full face value when the T-Bill matures. The return on investment comes from the difference between the purchase price and the face value.
Key Characteristics of T-Bills:
- Maturity: T-Bills typically mature in 4, 8, 13, 17, 26, or 52 weeks (one year or less).
- Discount Basis: They are sold at a price lower than their face value.
- No Coupon Payments: Investors do not receive regular interest payments.
- Low Risk: Backed by the full faith and credit of the U.S. government, making them virtually risk-free.
Why Calculate Different T-Bill Rates?
When evaluating T-Bills, you'll often encounter two primary rates: the Discount Rate (Bank Discount Yield) and the Investment Rate (Bond Equivalent Yield). These rates provide different perspectives on the T-Bill's return and are used for various purposes.
1. Discount Rate (Bank Discount Yield – BDY)
The Discount Rate is the traditional way T-Bills are quoted and is based on the face value of the bill. It represents the annualized percentage discount from the face value. This rate is commonly used in the money markets for quoting short-term instruments.
Formula:
Discount Rate = [(Face Value - Purchase Price) / Face Value] × (360 / Days to Maturity)
It's important to note that the Discount Rate uses a 360-day year convention, which is standard for many money market instruments but can make it less comparable to other investments that use a 365-day year.
2. Investment Rate (Bond Equivalent Yield – BEY)
The Investment Rate, also known as the Bond Equivalent Yield (BEY), provides a more accurate measure of the T-Bill's return, making it comparable to the yields on coupon-bearing bonds and other fixed-income securities. Unlike the Discount Rate, the BEY is based on the purchase price of the T-Bill and uses a 365-day year convention.
Formula:
Investment Rate = [(Face Value - Purchase Price) / Purchase Price] × (365 / Days to Maturity)
The BEY is generally higher than the Discount Rate because it annualizes the return over a 365-day year and bases the return on the actual amount invested (purchase price) rather than the face value.
How to Use the T-Bill Rate Calculator
Our T-Bill Rate Calculator simplifies the process of finding both the Discount Rate and Investment Rate. Here's how to use it:
- Face Value ($): Enter the face value of the T-Bill. This is the amount you will receive at maturity. T-Bills are typically issued in denominations of $1,000.
- Purchase Price ($): Input the price you paid for the T-Bill. This will be less than the face value.
- Days to Maturity: Enter the number of days remaining until the T-Bill matures.
- Click "Calculate T-Bill Rates" to see the results.
Example Calculation:
Let's say you purchase a T-Bill with a face value of $1,000 for a purchase price of $990, and it has 91 days until maturity.
- Face Value: $1,000
- Purchase Price: $990
- Days to Maturity: 91
Using the formulas:
Discount Rate:
[(1000 - 990) / 1000] × (360 / 91)
[10 / 1000] × 3.9560
0.01 × 3.9560 = 0.039560 or 3.9560%
Investment Rate:
[(1000 - 990) / 990] × (365 / 91)
[10 / 990] × 4.010989
0.010101 × 4.010989 = 0.040515 or 4.0515%
As you can see, the Investment Rate (BEY) provides a slightly higher and often more relevant yield for comparison with other investment opportunities.