Calculate the Bank Discount Yield and Bond Equivalent Yield (Investment Rate) based on your purchase price.
The amount received at maturity (usually $100 increments).
The actual amount you paid for the bill.
Number of days until the T-Bill matures.
Please enter valid positive numbers. Purchase price must be lower than Face Value.
Return on Investment (Profit):
Bank Discount Yield (Annualized):
Bond Equivalent Yield (Investment Rate):
*This is the rate comparable to APY on savings accounts.
function calculateTBillRate() {
// 1. Get input values
var faceValue = parseFloat(document.getElementById('tb_faceValue').value);
var purchasePrice = parseFloat(document.getElementById('tb_purchasePrice').value);
var daysToMaturity = parseInt(document.getElementById('tb_daysToMaturity').value);
var errorDiv = document.getElementById('tb_error');
var resultsDiv = document.getElementById('tb_results');
// 2. Validation
if (isNaN(faceValue) || isNaN(purchasePrice) || isNaN(daysToMaturity) ||
faceValue <= 0 || purchasePrice <= 0 || daysToMaturity = faceValue) {
errorDiv.style.display = 'block';
resultsDiv.style.display = 'none';
errorDiv.innerText = "Purchase Price usually must be lower than Face Value for Treasury Bills (Discount Instruments).";
return;
}
errorDiv.style.display = 'none';
// 3. Calculation Logic
// Calculate the raw discount amount (Profit)
var discountAmount = faceValue – purchasePrice;
// Calculate Bank Discount Yield (Uses 360-day year basis)
// Formula: (Discount / Face Value) * (360 / Days to Maturity)
var discountYield = (discountAmount / faceValue) * (360 / daysToMaturity) * 100;
// Calculate Bond Equivalent Yield / Investment Rate (Uses 365-day year basis – standard approximation)
// Formula: (Discount / Purchase Price) * (365 / Days to Maturity)
// Note: In leap years, 366 is sometimes used, but 365 is standard for calculators.
var investmentRate = (discountAmount / purchasePrice) * (365 / daysToMaturity) * 100;
// 4. Output Display
document.getElementById('res_profit').innerText = "$" + discountAmount.toFixed(2);
document.getElementById('res_discountYield').innerText = discountYield.toFixed(3) + "%";
document.getElementById('res_investmentRate').innerText = investmentRate.toFixed(3) + "%";
// Show results
resultsDiv.style.display = 'block';
}
Understanding T-Bill Rates: Discount vs. Investment Yield
Treasury Bills (T-Bills) differ from standard bonds because they are "zero-coupon" securities. They do not pay regular interest. Instead, they are sold at a discount to their face value (par value) and mature at the full face value. The difference between the purchase price and the face value represents the investor's return.
When analyzing T-Bills, you will encounter two primary rate metrics. Our T-Bill Rate Calculator computes both to help you compare investments accurately.
1. Bank Discount Yield (Discount Rate)
This is the rate typically quoted at Treasury auctions. It is calculated based on the Face Value of the bill and uses a 360-day banking year. While useful for institutional pricing, it often understates the actual return compared to other investments.
Formula: ((Face Value – Price) / Face Value) × (360 / Days to Maturity)
2. Bond Equivalent Yield (Investment Rate)
Also known as the Coupon Equivalent Yield, this metric is crucial for retail investors. It calculates the return based on the Purchase Price (the money you actually invested) and uses a 365-day calendar year. This rate allows you to directly compare T-Bills against savings accounts, CDs, or other bonds that quote an APY.
Formula: ((Face Value – Price) / Price) × (365 / Days to Maturity)
Example Calculation
Let's say you purchase a 26-week (182 days) T-Bill.
Face Value: $1,000
Purchase Price: $975.00
Profit: $25.00
Using the calculator above, you would find:
Bank Discount Yield: 4.945% (Based on $1,000 face value and 360 days)
Investment Rate (BEY): 5.143% (Based on $975 invested and 365 days)
Note: The Investment Rate is always higher than the Discount Rate because the denominator (Purchase Price) is lower than the Face Value, and the year is calculated as 365 days rather than 360.
Why Purchase Price Matters
The price of a T-Bill fluctuates based on market interest rates. When the Federal Reserve raises rates, new T-Bills are issued at higher yields, meaning their purchase prices (as a percentage of par) are lower. Conversely, when rates fall, T-Bills become more expensive to buy, resulting in lower yields.