.tb-calculator-container {
max-width: 800px;
margin: 20px auto;
padding: 25px;
background: #f9fbfd;
border: 1px solid #e1e4e8;
border-radius: 8px;
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
}
.tb-calc-title {
text-align: center;
color: #2c3e50;
margin-bottom: 20px;
font-size: 24px;
font-weight: 700;
}
.tb-input-group {
margin-bottom: 20px;
}
.tb-label {
display: block;
margin-bottom: 8px;
color: #34495e;
font-weight: 600;
}
.tb-input {
width: 100%;
padding: 12px;
border: 1px solid #cbd5e0;
border-radius: 6px;
font-size: 16px;
box-sizing: border-box;
transition: border-color 0.3s;
}
.tb-input:focus {
border-color: #3498db;
outline: none;
box-shadow: 0 0 0 3px rgba(52, 152, 219, 0.2);
}
.tb-btn {
width: 100%;
background-color: #2980b9;
color: white;
border: none;
padding: 15px;
font-size: 18px;
font-weight: bold;
border-radius: 6px;
cursor: pointer;
transition: background-color 0.3s;
}
.tb-btn:hover {
background-color: #2c3e50;
}
.tb-results {
margin-top: 25px;
background: #fff;
padding: 20px;
border-radius: 6px;
box-shadow: 0 2px 4px rgba(0,0,0,0.05);
display: none;
}
.tb-result-row {
display: flex;
justify-content: space-between;
padding: 12px 0;
border-bottom: 1px solid #eee;
}
.tb-result-row:last-child {
border-bottom: none;
}
.tb-result-label {
color: #7f8c8d;
}
.tb-result-value {
font-weight: 700;
color: #2c3e50;
}
.tb-highlight {
color: #27ae60;
font-size: 1.1em;
}
.tb-error {
color: #c0392b;
text-align: center;
margin-top: 10px;
display: none;
}
.tb-article-content {
max-width: 800px;
margin: 40px auto;
font-family: inherit;
line-height: 1.6;
color: #333;
}
.tb-article-content h2 {
color: #2c3e50;
margin-top: 30px;
border-bottom: 2px solid #ecf0f1;
padding-bottom: 10px;
}
.tb-article-content h3 {
color: #34495e;
margin-top: 25px;
}
.tb-formula-box {
background: #f1f8ff;
padding: 15px;
border-left: 4px solid #3498db;
font-family: "Courier New", monospace;
margin: 15px 0;
}
@media (max-width: 600px) {
.tb-calculator-container {
padding: 15px;
}
}
function calculateTBillRate() {
// Clear errors
var errorDiv = document.getElementById('tbErrorMessage');
var resultsDiv = document.getElementById('tbResultsSection');
errorDiv.style.display = 'none';
resultsDiv.style.display = 'none';
// Get Inputs
var faceValue = parseFloat(document.getElementById('tbFaceValue').value);
var purchasePrice = parseFloat(document.getElementById('tbPurchasePrice').value);
var days = parseInt(document.getElementById('tbDaysToMaturity').value);
// Validation
if (isNaN(faceValue) || isNaN(purchasePrice) || isNaN(days)) {
errorDiv.innerHTML = "Please enter valid numbers for all fields.";
errorDiv.style.display = 'block';
return;
}
if (days 366) {
errorDiv.innerHTML = "Days to maturity must be between 1 and 366.";
errorDiv.style.display = 'block';
return;
}
if (purchasePrice <= 0 || faceValue <= 0) {
errorDiv.innerHTML = "Price and Face Value must be greater than zero.";
errorDiv.style.display = 'block';
return;
}
// Logic
// 1. Discount Amount (Profit in dollars)
var discountAmount = faceValue – purchasePrice;
// 2. Bank Discount Yield (BDY)
// Formula: ((Face Value – Price) / Face Value) * (360 / Days)
var bankDiscountYield = (discountAmount / faceValue) * (360 / days) * 100;
// 3. Bond Equivalent Yield (BEY) or Investment Yield
// Formula: ((Face Value – Price) / Price) * (365 / Days)
// Note: T-Bills use 365 days (or 366 in leap year) for Investment Yield, vs 360 for Discount Yield.
// We will standardise to 365 for this calculator as is common convention for general estimates.
var bondEquivalentYield = (discountAmount / purchasePrice) * (365 / days) * 100;
// 4. Absolute ROI
var absoluteRoi = (discountAmount / purchasePrice) * 100;
// Output Formatting
document.getElementById('resDiscountAmount').innerText = "$" + discountAmount.toFixed(2);
document.getElementById('resDiscountYield').innerText = bankDiscountYield.toFixed(3) + "%";
document.getElementById('resBondYield').innerText = bondEquivalentYield.toFixed(3) + "%";
document.getElementById('resRoi').innerText = absoluteRoi.toFixed(2) + "%";
// Show Results
resultsDiv.style.display = 'block';
}
How is Treasury Bill Rate Calculated? A Complete Guide
Treasury Bills (T-Bills) are unique among fixed-income securities because they do not pay regular interest coupons. Instead, they are sold at a discount to their face value (par value). The "interest" you earn is actually the difference between the price you pay to buy the bill and the amount the government pays you when it matures.
Investors often get confused because T-Bill rates can be quoted in two different ways: the Bank Discount Yield and the Bond Equivalent Yield (Investment Yield). Use the calculator above to determine both metrics based on your purchase price.
Understanding the T-Bill Math
When you buy a T-Bill, you lend money to the government. If you buy a $1,000 T-Bill for $980, you are essentially lending the government $980 today, and they agree to pay you $1,000 at a specific future date.
- Face Value: The amount paid at maturity (e.g., $1,000).
- Purchase Price: The discounted price you pay today (e.g., $980).
- Discount Amount: Your profit (Face Value – Purchase Price).
Formula 1: Bank Discount Yield (BDY)
This is the rate most commonly quoted in financial news. It uses a 360-day year convention, which is a historical standard used by banks.
BDY = [(Face Value – Price) / Face Value] × (360 / Days to Maturity)
The limitation of the BDY is that it calculates return based on the face value, not the amount you actually invested, and uses a 360-day year. This typically makes the rate look slightly lower than your actual return on investment.
Formula 2: Bond Equivalent Yield (BEY)
Also known as the Investment Yield or Coupon Equivalent Yield. This metric allows you to compare T-Bills directly with traditional bonds that pay coupons. It uses the actual amount invested (Purchase Price) and a 365-day year.
BEY = [(Face Value – Price) / Purchase Price] × (365 / Days to Maturity)
Because the BEY divides by the lower Purchase Price (rather than the Face Value) and uses 365 days (rather than 360), the Investment Yield is mathematically higher than the Bank Discount Yield. This figure is a more accurate representation of your true annualized return.
Example Calculation
Let's say you purchase a 26-week (182-day) Treasury Bill with a face value of $10,000 for a price of $9,750.
Step 1: Calculate the Discount (Profit)
$10,000 (Face) – $9,750 (Price) = $250 profit.
Step 2: Calculate Bank Discount Yield
($250 / $10,000) × (360 / 182) = 0.025 × 1.978 = 4.945%
Step 3: Calculate Bond Equivalent Yield
($250 / $9,750) × (365 / 182) = 0.0256 × 2.005 = 5.132%
As you can see, the Bond Equivalent Yield (5.132%) is higher than the Discount Yield (4.945%), accurately reflecting the return on the cash you actually deployed.
Frequently Asked Questions
Why are there two different rates for T-Bills?
The "Discount Yield" is a convention for money market instruments to simplify calculations for banks using a 360-day year. The "Investment Yield" is provided to help investors compare T-Bills against other investments like CDs or Bonds which calculate interest based on a 365-day calendar year.
Does the days to maturity include the purchase date?
Usually, the days to maturity is calculated from the settlement date (when you pay) to the maturity date. It typically excludes the settlement date but includes the maturity date.
Why is the price lower than the face value?
Since T-Bills pay zero interest during their life, the price must be lower than the face value to provide a return to the investor. This mechanism is known as a "Zero Coupon" or "Deep Discount" bond structure.