How to Calculate Discount Rate of Treasury Bill

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Treasury Bill Discount Rate Calculator

Results:

Bank Discount Rate: 0.00%

Investment Rate (BEY): 0.00%

Total Discount: $0.00

function calculateTBillRate() { var face = parseFloat(document.getElementById('faceValue').value); var price = parseFloat(document.getElementById('purchasePrice').value); var days = parseFloat(document.getElementById('daysToMaturity').value); var resultsDiv = document.getElementById('tbill-results'); if (isNaN(face) || isNaN(price) || isNaN(days) || face <= 0 || price <= 0 || days = face) { alert("Purchase price must be lower than the face value for a discount T-Bill."); return; } // 1. Bank Discount Rate Formula: ((Face – Price) / Face) * (360 / Days) var discountRate = ((face – price) / face) * (360 / days) * 100; // 2. Investment Rate (Bond Equivalent Yield) Formula: ((Face – Price) / Price) * (365 / Days) var investmentRate = ((face – price) / price) * (365 / days) * 100; var totalDiscount = face – price; document.getElementById('discountRateResult').innerText = discountRate.toFixed(3); document.getElementById('investmentRateResult').innerText = investmentRate.toFixed(3); document.getElementById('totalDiscountResult').innerText = totalDiscount.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); resultsDiv.style.display = 'block'; }

Understanding Treasury Bill Discount Rates

Treasury Bills (T-Bills) are short-term debt obligations backed by the Treasury Department with maturities ranging from a few days to 52 weeks. Unlike standard bonds, T-Bills do not pay regular interest. Instead, they are sold at a discount to their face value. The difference between the purchase price and the face value represents the interest earned by the investor.

The Discount Rate Formula

The "Bank Discount Rate" is the standardized way the market quotes T-Bill yields. It uses a 360-day year convention. The formula is:

Discount Rate = [(Face Value – Purchase Price) / Face Value] × (360 / Days to Maturity)

Discount Rate vs. Investment Rate (BEY)

While the Bank Discount Rate is the standard quote, it often understates the actual return on investment. To compare a T-Bill to a traditional bond, investors use the Bond Equivalent Yield (BEY), also known as the Investment Rate. This calculation differs in two ways:

  • It uses the Purchase Price as the denominator (the actual money you invested).
  • It uses a 365-day year (or 366 for leap years) instead of 360.

Calculation Example

Suppose you purchase a 91-day T-Bill with a Face Value of $10,000 for a Price of $9,850.

  1. Total Discount: $10,000 – $9,850 = $150.
  2. Discount Rate: ($150 / $10,000) × (360 / 91) = 0.015 × 3.956 = 5.934%.
  3. Investment Rate (BEY): ($150 / $9,850) × (365 / 91) = 0.01522 × 4.011 = 6.106%.

Note how the Investment Rate is higher; this provides a more accurate picture of your actual yield relative to the cash you spent.

Why This Matters for Investors

Investors use these calculations to compare T-Bills against other short-term instruments like Certificates of Deposit (CDs) or Money Market funds. Because T-Bills are considered "risk-free" (backed by the government), their discount rates serve as a benchmark for all other short-term interest rates in the economy.

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