3 Month Treasury Bill Calculator

Calculate the yield, price, and potential returns for your 3-month T-Bill investment.

T-Bill Investment Summary

Metric	Value
Par Value	$0.00
Discount Rate	0.00%
Days to Maturity	0
Purchase Price	$0.00
Total Interest Earned	$0.00
Yield to Maturity (BEY)	0.00%

This comprehensive guide explains the 3 month treasury bill calculator, its underlying principles, and how it helps investors make informed decisions about short-term U.S. government debt.

What is a 3 Month Treasury Bill?

A 3-month Treasury Bill (T-Bill) is a short-term debt instrument issued by the U.S. Department of the Treasury. It represents a loan made by an investor to the U.S. government for a period of approximately three months. T-Bills are considered among the safest investments in the world due to the backing of the U.S. government, making them a popular choice for preserving capital and earning a modest return over a short timeframe. They are sold at a discount to their face value (par value) and the investor receives the full face value at maturity. The difference between the purchase price and the face value represents the investor's earnings.

Who should use a 3 month treasury bill calculator?

• Short-term Investors: Individuals or institutions looking for a safe place to park cash for a few months while earning a predictable return.
• Risk-Averse Investors: Those who prioritize capital preservation over high growth and want to avoid market volatility.
• Portfolio Diversifiers: Investors seeking to add a low-risk, liquid asset to their broader investment portfolio.
• Cash Management: Businesses needing to manage short-term cash surpluses effectively.

Common Misconceptions:

• T-Bills are "Interest-Bearing": While they generate returns, T-Bills are technically sold at a discount and pay the face value at maturity, rather than paying periodic interest like bonds. The return is implicit in the price difference.
• T-Bills are Risk-Free: While credit risk is virtually non-existent due to U.S. government backing, investors can still face reinvestment risk (if rates fall when the T-Bill matures) and inflation risk (if inflation erodes the purchasing power of the return).
• All T-Bills are the Same: Maturities vary (4-week, 8-week, 13-week, 17-week, 26-week, 52-week). The 3-month T-Bill specifically refers to the 13-week issuance.

3 Month Treasury Bill Calculator Formula and Mathematical Explanation

The 3 month treasury bill calculator utilizes standard formulas to determine the key financial metrics of a T-Bill investment. The primary calculations involve determining the purchase price and then annualizing the return to express it as a yield.

Step-by-Step Derivation:

1. Calculate the Discount Amount: This is the total amount of discount based on the annual rate and the T-Bill's term. The U.S. Treasury uses a 360-day year convention for T-Bill discount calculations.
   Discount Amount = Par Value * (Discount Rate * Days to Maturity / 360)
2. Calculate the Purchase Price: The purchase price is the par value minus the discount amount.
   Purchase Price = Par Value - Discount Amount
   Alternatively, this can be expressed directly as:
   Purchase Price = Par Value * (1 - (Discount Rate * Days to Maturity / 360))
3. Calculate the Total Interest Earned: This is simply the difference between the par value and the purchase price.
   Total Interest Earned = Par Value - Purchase Price
4. Calculate the Yield to Maturity (Bond Equivalent Yield – BEY): This is the most common way to express the return on a T-Bill, as it annualizes the return on a 365-day basis and is comparable to yields on other fixed-income securities.
   Yield to Maturity (BEY) = ((Par Value - Purchase Price) / Purchase Price) * (365 / Days to Maturity)
   This formula essentially calculates the holding period return and then scales it up to a full year.

Variable Explanations:

T-Bill Calculation Variables

Variable	Meaning	Unit	Typical Range
Par Value	The face value of the Treasury Bill, paid to the investor at maturity.	Currency (e.g., USD)	$100, $1,000, $5,000, $10,000 (common denominations)
Discount Rate	The annualized rate at which the T-Bill is sold at a discount to its par value. Based on a 360-day year convention.	Percentage (%)	0.1% – 6.0% (fluctuates with market conditions and Fed policy)
Days to Maturity	The number of days remaining until the T-Bill matures and the investor receives the par value.	Days	Typically 85-91 days for a 3-month T-Bill, but can be up to 365 days for other T-Bill tenors.
Purchase Price	The actual amount paid by the investor to acquire the T-Bill. It's less than the par value.	Currency (e.g., USD)	Slightly less than Par Value
Total Interest Earned	The profit made by the investor, which is the difference between the par value and the purchase price.	Currency (e.g., USD)	Positive value, dependent on other inputs
Yield to Maturity (BEY)	The annualized rate of return an investor can expect if they hold the T-Bill until maturity. Expressed on a 365-day basis.	Percentage (%)	Similar range to Discount Rate, but calculated differently.

Practical Examples (Real-World Use Cases)

Example 1: Standard 3-Month T-Bill Purchase

An investor wants to invest $1,000 for three months and finds a 13-week T-Bill with a discount rate of 4.50%.

• Inputs:
  • Par Value: $1,000
  • Discount Rate: 4.50%
  • Days to Maturity: 91
• Calculation:
  • Discount Amount = $1,000 * (0.0450 * 91 / 360) = $11.41
  • Purchase Price = $1,000 – $11.41 = $988.59
  • Total Interest Earned = $1,000 – $988.59 = $11.41
  • Yield to Maturity (BEY) = (($1,000 – $988.59) / $988.59) * (365 / 91) = (0.011555 / 0.98859) * 4.010989 ≈ 4.61%
• Interpretation: The investor pays $988.59 for the T-Bill and receives $1,000 after 91 days, earning $11.41 in interest. The annualized yield on this investment is approximately 4.61%. This is a safe way to earn a return slightly higher than the stated discount rate.

Example 2: Higher Rate Environment

In a period of rising interest rates, an investor considers a 3-month T-Bill with a higher discount rate of 5.25% for a $10,000 investment.

• Inputs:
  • Par Value: $10,000
  • Discount Rate: 5.25%
  • Days to Maturity: 90
• Calculation:
  • Discount Amount = $10,000 * (0.0525 * 90 / 360) = $131.25
  • Purchase Price = $10,000 – $131.25 = $9,868.75
  • Total Interest Earned = $10,000 – $9,868.75 = $131.25
  • Yield to Maturity (BEY) = (($10,000 – $9,868.75) / $9,868.75) * (365 / 90) = ($131.25 / $9,868.75) * 4.05555 ≈ 5.39%
• Interpretation: The investor purchases the T-Bill for $9,868.75 and will receive $10,000 at maturity, yielding $131.25 in profit. The annualized return (BEY) is approximately 5.39%. This demonstrates how higher discount rates translate to better yields, especially attractive in a rising rate environment.

How to Use This 3 Month Treasury Bill Calculator

Our 3 month treasury bill calculator is designed for simplicity and accuracy. Follow these steps to understand your potential T-Bill returns:

1. Enter Par Value: Input the face value of the T-Bill you are considering. Common denominations are $1,000 or $10,000.
2. Input Discount Rate: Enter the annual discount rate quoted for the T-Bill. Ensure you use the percentage value (e.g., 4.5 for 4.50%).
3. Specify Days to Maturity: Enter the exact number of days until the T-Bill matures. For a standard 3-month T-Bill, this is typically around 91 days.
4. Click 'Calculate': The calculator will instantly display your key results.

How to Read Results:

• Purchase Price: This is the amount you will pay upfront to buy the T-Bill. It will always be less than the Par Value.
• Total Interest Earned: The dollar amount of profit you will receive at maturity.
• Yield to Maturity (BEY): This is the most important metric for comparing T-Bill returns to other investments. It represents the annualized percentage return.

Decision-Making Guidance: Use the calculated Yield to Maturity (BEY) to compare the T-Bill's return against other short-term investment options, such as high-yield savings accounts, money market funds, or certificates of deposit (CDs). Consider the safety and liquidity offered by T-Bills when making your decision.

Key Factors That Affect 3 Month Treasury Bill Results

Several factors influence the outcome of a 3-month Treasury Bill investment and the results shown by the calculator:

1. Federal Reserve Monetary Policy: The Federal Reserve's target interest rate significantly impacts short-term rates. When the Fed raises rates, T-Bill yields tend to increase, and vice versa. This directly affects the discount rate offered.
2. Market Demand and Supply: Like any security, T-Bill prices (and thus yields) are influenced by the balance of buyers and sellers. High demand can push prices up and yields down, while low demand has the opposite effect.
3. Inflation Expectations: If investors anticipate higher inflation, they will demand higher yields to compensate for the erosion of purchasing power. This pushes up the discount rates on T-Bills.
4. Economic Outlook: Broader economic conditions, such as GDP growth, employment figures, and consumer confidence, influence investor sentiment and the perceived safety of government debt, affecting yields.
5. Treasury Auction Timing: T-Bills are sold at regular auctions. The specific yield determined at auction is crucial. Our calculator uses a provided discount rate, but the actual auction rate is market-determined.
6. Liquidity Needs: While T-Bills are highly liquid, holding them to maturity guarantees the calculated return. Early sale might incur price fluctuations based on prevailing market rates, impacting the final outcome.
7. Taxation: Interest earned on Treasury securities is subject to federal income tax but exempt from state and local income taxes. This tax treatment can affect the *after-tax* yield compared to other investments.

Frequently Asked Questions (FAQ)

Q1: Are 3-month T-Bills safe?

A1: Yes, 3-month T-Bills are considered extremely safe because they are backed by the full faith and credit of the U.S. government, making the risk of default virtually zero.

Q2: How is the Yield to Maturity (BEY) different from the Discount Rate?

A2: The Discount Rate is the annualized rate used to calculate the T-Bill's purchase price, based on a 360-day year. The Yield to Maturity (Bond Equivalent Yield) is a more standardized measure that annualizes the return on a 365-day basis, making it comparable to other fixed-income investments.

Q3: Can I lose money on a 3-month T-Bill?

A3: If held to maturity, you cannot lose the principal amount invested, as you receive the full par value. However, the *real return* can be negative if inflation is higher than the yield earned. Selling before maturity could result in a loss if interest rates have risen significantly.

Q4: How do I buy a 3-month T-Bill?

A4: You can purchase T-Bills directly from the U.S. Treasury via TreasuryDirect.gov or through a bank or brokerage firm. TreasuryDirect is often preferred for direct purchases to avoid fees.

Q5: What is the 360-day convention for T-Bills?

A5: The U.S. Treasury uses a 360-day year for calculating the discount on T-Bills. This is a convention that slightly increases the effective yield compared to using a 365-day year for the discount calculation itself.

Q6: Are T-Bill earnings taxable?

A6: Interest earned on T-Bills is subject to federal income tax but is exempt from state and local income taxes. This can be a significant advantage for investors in high-tax states.

Q7: What happens if I need the money before maturity?

A7: You can sell your T-Bill on the secondary market before it matures. The price you receive will depend on current market interest rates. If rates have risen since you bought the T-Bill, its price may have fallen, potentially resulting in a loss.

Q8: How do T-Bill yields compare to savings accounts?

A8: T-Bill yields often track short-term interest rates, similar to high-yield savings accounts or money market funds. T-Bills offer government backing and state/local tax exemption, which can make their after-tax yield more attractive in certain scenarios.