How to Calculate T-bill Discount Rate

T-Bill Discount Rate Calculator

Calculate the annualized discount rate and investment yield of a Treasury Bill.

Face Value (Par Value)

The amount paid at maturity (usually $100, $1,000, etc.).

Purchase Price

Days to Maturity Actual number of days until the T-Bill matures.

Bank Discount Rate 0.00% Based on 360-day year

Bond Equivalent Yield 0.00% Based on 365-day year

Discount Amount: $0.00

function calculateTBillRate() { // Get inputs var faceValue = parseFloat(document.getElementById('tbill_face_value').value); var purchasePrice = parseFloat(document.getElementById('tbill_purchase_price').value); var daysMaturity = parseFloat(document.getElementById('tbill_days_maturity').value); // Validation if (isNaN(faceValue) || isNaN(purchasePrice) || isNaN(daysMaturity) || daysMaturity = faceValue) { alert("Purchase price represents a discount, so it should generally be lower than the Face Value."); } // Calculation Logic // 1. Discount Amount var discountAmount = faceValue – purchasePrice; // 2. Bank Discount Rate Formula: ((Face – Price) / Face) * (360 / Days) var bankDiscountRate = (discountAmount / faceValue) * (360 / daysMaturity) * 100; // 3. Investment Rate (Bond Equivalent Yield) Formula: ((Face – Price) / Price) * (365 / Days) // Note: Investment rate uses 365 days (or 366) and divides by the Purchase Price, not Face Value. var investmentRate = (discountAmount / purchasePrice) * (365 / daysMaturity) * 100; // Update DOM document.getElementById('display_discount_rate').innerHTML = bankDiscountRate.toFixed(3) + '%'; document.getElementById('display_investment_rate').innerHTML = investmentRate.toFixed(3) + '%'; document.getElementById('display_discount_amount').innerHTML = '$' + discountAmount.toFixed(2); // Show result area document.getElementById('tbill_result_area').style.display = 'block'; }

Treasury Bills (T-Bills) are short-term debt securities issued by the U.S. government. Unlike traditional bonds that pay regular interest coupons, T-Bills are sold at a discount to their face value (par value). The investor's return is the difference between the purchase price and the face value paid at maturity.

There are two primary ways to express the return on a T-Bill: the Bank Discount Rate and the Investment Rate (also known as the Bond Equivalent Yield). Understanding the difference is crucial for accurately comparing T-Bills against other investment options.

1. The Bank Discount Rate Formula

The discount rate is the standard metric used when T-Bills are quoted in the market. It is annualized based on a 360-day banker's year and is calculated as a percentage of the Face Value.

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

Face Value: The value of the bill at maturity (e.g., $1,000).
Purchase Price: The discounted price you pay today.
Days to Maturity: The number of days remaining until the bill matures.
360: The standard "banker's year" used for money market calculations.

2. The Investment Rate (Bond Equivalent Yield)

The Investment Rate is often considered a more accurate reflection of your actual Return on Investment (ROI). It differs from the discount rate in two ways: it uses the Purchase Price in the denominator (since that is your actual invested capital), and it uses a 365-day calendar year.

            Investment Rate = [(Face Value – Purchase Price) / Purchase Price] × (365 / Days to Maturity)
        

This yield allows you to compare T-Bills directly with other securities that pay coupons, such as T-Notes or corporate bonds.

Example Calculation

Let's assume you want to purchase a 182-day Treasury Bill with a face value of $10,000. The auction price is $9,750.

Step 1: Calculate the Discount Amount
$10,000 – $9,750 = $250

Step 2: Calculate Bank Discount Rate
($250 / $10,000) × (360 / 182) = 0.025 × 1.978 = 4.945%

Step 3: Calculate Investment Rate (Bond Equivalent Yield)
($250 / $9,750) × (365 / 182) = 0.0256 × 2.005 = 5.143%

As you can see, the Investment Rate (5.143%) is higher than the Discount Rate (4.945%). This is typical because the investment rate is calculated on the lower purchase price rather than the higher face value, and it accounts for 5 extra days of interest accrual in a year.

Key Factors Influencing T-Bill Rates

When calculating T-Bill rates, keep the following in mind:

Federal Reserve Policy: The Fed Funds Rate heavily influences short-term T-Bill yields.
Inflation Expectations: Higher inflation generally leads to higher discount rates to compensate investors for lost purchasing power.
Time to Maturity: Longer-term bills (e.g., 52-week) usually offer higher rates than shorter-term bills (e.g., 4-week) due to maturity risk, though inverted yield curves can reverse this.

T-Bill Discount Rate Calculator