A Treasury Bill (T-Bill) is a short-term debt instrument issued by the U.S. Department of the Treasury. They are sold at a discount from their face value and mature at their face value, with the difference representing the investor's earnings. This calculator helps you determine the effective annual yield of a T-Bill based on its purchase price, face value, and time to maturity.
The Effective Annual Yield is: %
function calculateTBillYield() {
var purchasePrice = parseFloat(document.getElementById("purchasePrice").value);
var faceValue = parseFloat(document.getElementById("faceValue").value);
var daysToMaturity = parseFloat(document.getElementById("daysToMaturity").value);
var resultDiv = document.getElementById("result");
var annualYieldSpan = document.getElementById("annualYield");
if (isNaN(purchasePrice) || isNaN(faceValue) || isNaN(daysToMaturity) ||
purchasePrice <= 0 || faceValue <= 0 || daysToMaturity = faceValue) {
alert("Please enter valid positive numbers for all fields, and ensure Purchase Price is less than Face Value.");
resultDiv.style.display = "none";
return;
}
// Calculate the discount amount
var discountAmount = faceValue – purchasePrice;
// Calculate the holding period yield (fraction of the year)
// There are 360 days in a T-bill year for discount rate calculations
var holdingPeriodYield = (discountAmount / purchasePrice) * (daysToMaturity / 360);
// Calculate the effective annual yield
// This is the T-bill discount yield annualized
var annualYield = holdingPeriodYield * (365 / daysToMaturity);
annualYieldSpan.textContent = annualYield.toFixed(4);
resultDiv.style.display = "block";
}
Understanding Treasury Bills and Yield Calculation
Treasury Bills (T-Bills) are short-term debt obligations of the U.S. government with maturities of one year or less. They are considered one of the safest investments in the world due to the backing of the U.S. Treasury. T-Bills are typically sold at a discount to their face value (e.g., a $100 T-Bill might be sold for $98.50). When the T-Bill matures, the holder receives the full face value. The difference between the purchase price and the face value represents the investor's profit, which is essentially the interest earned.
Calculating the effective annual yield helps investors understand the true return on their T-Bill investment over a full year, even if the bill matures in less than a year. The formula used in this calculator is as follows:
Discount Amount: This is the difference between the T-Bill's face value and its purchase price (Face Value – Purchase Price).
Holding Period Yield: This is the return earned over the specific period the T-Bill is held until maturity. It's calculated as (Discount Amount / Purchase Price) multiplied by the fraction of a year the T-Bill has to maturity (Days to Maturity / 360). The 360-day convention is commonly used for T-Bill discount calculations.
Effective Annual Yield: To annualize the holding period yield, we multiply it by the ratio of days in a year (365) to the days to maturity. This gives us the equivalent yield if the investment were held for a full 365 days.
Example:
Suppose you purchase a T-Bill with a face value of $100.00 for $98.50, and it has 91 days until maturity.