3 Month T-bill Calculator

An essential tool to calculate the return on your 3-month Treasury Bill investments.

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Yield vs. Discount Rate

Discount Rate (%)	Purchase Price ($)	Annualized Yield (BEY) (%)

This table illustrates how the purchase price and annualized yield change with variations in the discount rate, providing insight into the market for the {primary_keyword}.

What is a 3-Month T-Bill?

A 3-month Treasury Bill (T-Bill) is a short-term debt security issued by the U.S. Department of the Treasury. It has a maturity of 91 days (approximately 3 months). Unlike traditional bonds, T-Bills do not pay periodic interest. Instead, they 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 received at maturity. This makes the {primary_keyword} an essential tool for investors.

These securities are considered one of the safest investments in the world because they are backed by the full faith and credit of the U.S. government. They are a popular choice for investors seeking a low-risk way to preserve capital and earn a predictable return over a short period. Common users include individual investors, corporations with short-term cash management needs, and institutional funds. A common misconception is that the discount rate is the same as the actual yield; however, as our {primary_keyword} shows, the true annualized yield is slightly different.

{primary_keyword} Formula and Mathematical Explanation

Calculating the returns on a 3-month T-Bill involves two main steps. First, we determine the purchase price from the discount rate. Second, we calculate the Bond Equivalent Yield (BEY) to annualize the return for comparison purposes.

Step 1: Calculate Purchase Price (P)
The price is found by applying the discount rate to the face value for the 91-day period. The formula uses a 360-day year, as is standard for money market instruments.
P = FV * (1 - (D * (n / 360)))

Step 2: Calculate Bond Equivalent Yield (BEY)
The BEY annualizes the return based on the purchase price and uses a 365-day year, allowing for a more accurate comparison with other bonds.
BEY = ((FV - P) / P) * (365 / n)

Variable	Meaning	Unit	Typical Range
FV	Face Value	Dollars ($)	$1,000+
D	Discount Rate	Percent (%)	0.1% – 8%
P	Purchase Price	Dollars ($)	Less than FV
n	Days to Maturity	Days	91 (for a 3-month T-Bill)
BEY	Bond Equivalent Yield	Percent (%)	Similar to D

Practical Examples (Real-World Use Cases)

Example 1: Conservative Investor

An investor wants to park $50,000 in a safe asset for 3 months. They participate in a T-Bill auction and secure bills with a face value of $50,000 at a discount rate of 4.5%.

• Inputs: Face Value = $50,000, Discount Rate = 4.5%
• Purchase Price: Using the {primary_keyword} formula, the price is $50,000 * (1 – (0.045 * 91 / 360)) = $49,431.25.
• Total Gain: $50,000 – $49,431.25 = $568.75.
• Annualized Yield (BEY): (($568.75 / $49,431.25) * (365 / 91)) = 4.61%.
• Interpretation: The investor pays $49,431.25 and receives $50,000 back in three months, earning a total of $568.75. This represents an annualized return of 4.61%, which they can compare to other investments like a {related_keywords}.

Example 2: Corporate Treasurer

A company has $1 million in cash that it won’t need for the next quarter. To earn some return, the treasurer uses a {primary_keyword} to evaluate an investment in 3-month T-Bills. The current auction clears at a discount rate of 5.1%.

• Inputs: Face Value = $1,000,000, Discount Rate = 5.1%
• Purchase Price: $1,000,000 * (1 – (0.051 * 91 / 360)) = $987,125.
• Total Gain: $1,000,000 – $987,125 = $12,875.
• Annualized Yield (BEY): (($12,875 / $987,125) * (365 / 91)) = 5.23%.
• Interpretation: The company invests just under $987k and secures a guaranteed return of nearly $13k in 91 days. The 5.23% BEY is attractive for its safety and liquidity. This is a better return than a standard {related_keywords} might offer.

How to Use This {primary_keyword} Calculator

Using our {primary_keyword} is straightforward. Follow these steps to determine your potential returns:

1. Enter the Face Value: This is the total par value of the T-Bills you are purchasing. It’s the amount you will be paid at maturity.
2. Enter the Discount Rate: This is the annualized rate you receive your T-Bills at, determined at auction. Input it as a percentage.
3. Review the Results: The calculator automatically updates. The primary result is the Annualized Yield (BEY), which is the most accurate measure of your return. You can also see the exact Purchase Price you’ll pay, the Total Gain in dollars, and the simple Return for the Period.
4. Analyze the Chart and Table: The dynamic chart and table provide deeper insights. The chart visualizes your initial investment versus your matured return. The table shows how different discount rates impact your yield, helping you understand the results of a potential {primary_keyword} across various scenarios.

Key Factors That Affect 3-Month T-Bill Results

The return you get from a 3-month T-Bill isn’t arbitrary. Several economic factors influence the discount rates at auction, which the {primary_keyword} uses for its calculations. Understanding them helps in making informed investment decisions, perhaps comparing them with returns from a {related_keywords}.

• Federal Reserve’s Monetary Policy: The Federal Funds Rate, set by the Fed, is the primary driver of all short-term interest rates. When the Fed raises rates, T-bill yields tend to follow, making them more attractive.
• Inflation Expectations: If investors expect inflation to rise, they will demand higher yields to compensate for the decrease in purchasing power. High inflation often leads to higher T-bill rates.
• Economic Growth: In a strong economy, demand for money increases, which can push interest rates up. Conversely, in a weak economy, the Fed may lower rates to stimulate growth, causing T-bill yields to fall.
• Market Demand and Supply (Safe Haven Status): During periods of economic uncertainty or stock market volatility, investors often flock to the safety of T-bills. This increased demand can push prices up and, consequently, drive yields down. This is a key reason to use a {primary_keyword}.
• Geopolitical Risk: Global instability can increase the demand for safe U.S. government debt, acting similarly to general market volatility and lowering yields.
• Treasury Department Issuance: The amount of debt the Treasury needs to issue can also affect rates. A larger supply of T-bills might require slightly higher yields to attract enough buyers. It’s always wise to check different investment options, such as a {related_keywords}.

Frequently Asked Questions (FAQ)

1. Are 3-month T-bills a good investment?

They are an excellent investment for capital preservation and short-term savings goals due to their high safety and liquidity. They may not be suitable for long-term growth, as their returns are typically lower than stocks. Using a {primary_keyword} helps assess their return potential.

2. Do I pay taxes on T-Bill earnings?

Yes. Earnings are subject to federal income tax but are exempt from all state and local income taxes, which can be a significant advantage for investors in high-tax states.

3. What is the difference between discount rate and yield?

The discount rate is used to calculate the purchase price based on the face value. The yield (BEY) is the actual annualized return based on the price you paid. The yield is a more accurate measure of your investment return, as calculated by this {primary_keyword}.

4. Where can I buy 3-month T-Bills?

You can buy them directly from the U.S. government through the TreasuryDirect website or through a bank or brokerage account.

5. What happens at maturity?

At maturity, the full face value of the T-Bill is automatically deposited into your account. You can then choose to reinvest the proceeds into a new T-Bill or withdraw the cash.

6. Can I sell a T-Bill before it matures?

Yes, T-Bills can be sold on the secondary market through a broker before their maturity date. The price you receive will depend on prevailing interest rates at the time of sale.

7. What is the minimum investment for a T-Bill?

The minimum purchase amount is typically $100, and they are sold in increments of $100.

8. Why does the {primary_keyword} use 91 days?

A “3-month” T-Bill actually has a 13-week maturity cycle, which equals 91 days. This is the standard term used for these specific securities.