3 Month Treasury Bill Calculator

3-Month Treasury Bill Calculator

function calculateTBill() { var faceValue = parseFloat(document.getElementById('faceValue').value); var discountRate = parseFloat(document.getElementById('discountRate').value); var daysToMaturity = parseFloat(document.getElementById('daysToMaturity').value); if (isNaN(faceValue) || isNaN(discountRate) || isNaN(daysToMaturity) || faceValue <= 0 || discountRate < 0 || daysToMaturity <= 0) { document.getElementById('purchasePriceResult').innerText = 'Please enter valid positive numbers.'; document.getElementById('discountAmountResult').innerText = ''; document.getElementById('investmentYieldResult').innerText = ''; return; } // Convert discount rate from percentage to decimal var discountRateDecimal = discountRate / 100; // Calculate Discount Amount // Formula: Discount Amount = Face Value * (Annualized Discount Rate) * (Days to Maturity / 360) var discountAmount = faceValue * discountRateDecimal * (daysToMaturity / 360); // Calculate Purchase Price // Formula: Purchase Price = Face Value – Discount Amount var purchasePrice = faceValue – discountAmount; // Calculate Annualized Investment Yield // Formula: Investment Yield = (Discount Amount / Purchase Price) * (365 / Days to Maturity) * 100 var investmentYield = (discountAmount / purchasePrice) * (365 / daysToMaturity) * 100; document.getElementById('purchasePriceResult').innerText = '$' + purchasePrice.toFixed(2); document.getElementById('discountAmountResult').innerText = '$' + discountAmount.toFixed(2); document.getElementById('investmentYieldResult').innerText = investmentYield.toFixed(2) + '%'; }

Understanding the 3-Month Treasury Bill Calculator

Treasury Bills (T-Bills) are short-term debt instruments issued by the U.S. Department of the Treasury to finance government spending. They are considered one of the safest investments because they are backed by the full faith and credit of the U.S. government. Unlike bonds that pay periodic interest, T-Bills are sold at a discount from their face value and mature at their full face value.

How 3-Month T-Bills Work

A 3-month T-Bill typically has a maturity period of around 91 days. When you purchase a T-Bill, you pay less than its face value (the amount you'll receive at maturity). The difference between the purchase price and the face value is your return, known as the discount amount. This return is often expressed as an annualized discount rate or an annualized investment yield.

Using This Calculator

This calculator helps you understand the financial aspects of investing in a 3-month Treasury Bill. By inputting the T-Bill's face value, the annualized discount rate, and the exact days to maturity, you can determine the purchase price, the actual discount amount you'll earn, and the annualized investment yield.

Key Terms Explained:

• Face Value of T-Bill ($): This is the par value of the T-Bill, the amount you will receive when the T-Bill matures. Common face values are $1,000, $5,000, $10,000, etc.
• Annualized Discount Rate (%): This is the rate at which the T-Bill is sold at a discount, expressed as an annual percentage. It's the rate often quoted in financial markets.
• Days to Maturity: The exact number of days remaining until the T-Bill matures. For a 3-month T-Bill, this is typically around 91 days, but can vary slightly depending on the issuance date.
• Purchase Price ($): The actual amount you pay to acquire the T-Bill. This will be less than the face value.
• Discount Amount ($): The profit you make from the T-Bill, calculated as the Face Value minus the Purchase Price.
• Annualized Investment Yield (%): This is the true annualized rate of return on your investment, based on the purchase price. It often differs slightly from the annualized discount rate because it's calculated based on the price you paid and typically uses a 365-day year for annualization, whereas the discount rate uses a 360-day year.

Example Calculation:

Let's say you are considering a 3-month T-Bill with the following characteristics:

• Face Value: $10,000
• Annualized Discount Rate: 5.25%
• Days to Maturity: 91 days

Using the calculator:

1. Discount Amount: $10,000 * (0.0525) * (91 / 360) = $132.81
2. Purchase Price: $10,000 – $132.81 = $9,867.19
3. Annualized Investment Yield: ($132.81 / $9,867.19) * (365 / 91) * 100 = 5.39%

This means you would pay $9,867.19 for the T-Bill and receive $10,000 at maturity, earning a profit of $132.81, which translates to an annualized investment yield of 5.39%.