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Enter your values and select Calculate.
What this calculator shows
A Treasury bill (T-bill) pays no coupon. You buy it for less than its face value and receive the full face value at maturity; the difference is your interest. This calculator turns a bill’s face value, price (or discount) and term into:
- Discount amount: your dollar return if you hold the bill to maturity.
- Total return over the term: the discount divided by the price you paid.
- Discount rate, also called the bank discount yield.
- Investment rate, also called the coupon-equivalent or bond-equivalent yield.
- Effective annual yield: the term return compounded over a year, for comparison with accounts that quote an APY.
The formulas
The calculator follows the formulas TreasuryDirect publishes for bills. F is the face value, P the price, t the number of days to maturity and y the number of days in the year (365, or 366 when the year following the issue date contains February 29).
Discount rate
d = (F − P) ÷ F × 360 ÷ t
The discount rate measures the discount as a share of face value and annualizes it over a 360-day year. It is the rate quoted in bill auction results and is always lower than the investment rate for the same bill.
Investment rate for bills of half a year or less
i = (F − P) ÷ P × y ÷ t
The investment rate measures the return on the price you paid and annualizes it over an actual-day year, which makes it comparable with yields on Treasury notes and bonds.
Investment rate for bills longer than half a year
For bills that mature in more than half a year, such as 52-week bills, the Treasury uses a formula that accounts for the semiannual interest a note would pay:
i = [ −2t/y + 2 × √( (t/y)² − (2t/y − 1)(1 − 100/P) ) ] ÷ (2t/y − 1)
Here P is the price per $100 of face value. The calculator switches formulas automatically and tells you which one it used.
Price from a discount rate
P = F × (1 − d × t ÷ 360)
Choose “Discount rate” above if you know an auction’s discount rate and want the price and investment rate.
Worked example
Suppose you buy a 13-week bill (91 days) with a face value of $100,000 for $98,450.
- Discount amount: $100,000 − $98,450 = $1,550
- Total return: $1,550 ÷ $98,450 = 1.574% over 91 days
- Discount rate: $1,550 ÷ $100,000 × 360 ÷ 91 = 6.132%
- Investment rate (365-day year): $1,550 ÷ $98,450 × 365 ÷ 91 = 6.315%
- Effective annual yield: ($100,000 ÷ $98,450)365/91 − 1 = 6.466%
These are example numbers chosen to make the arithmetic easy to follow, not current market rates. Enter them into the calculator to check the results.
Assumptions and rounding
- You hold the bill until it matures. Selling earlier means receiving the market price that day, which may be higher or lower.
- Taxes are not included. T-bill interest is subject to federal income tax and exempt from state and local income taxes.
- Fees, commissions and reinvestment are not included.
- Calculations use full precision. Rates are displayed to three decimal places and dollar amounts to the cent, so a hand calculation with rounded inputs may differ in the last digit.
- If you do not enter an issue date, a 365-day year is used for the investment rate.
Discount rate or investment rate: which should I use?
Use the investment rate when comparing a bill with other investments, such as notes, CDs or savings accounts, because it is based on the money you actually invest and a full calendar year. Use the discount rate when reading auction announcements or quotes that use it. Never compare a discount rate with another product’s yield directly; it understates the return.
The daily 3-month Treasury rate on this site is a par yield curve rate on a bond-equivalent basis, which is closest in concept to the investment rate.
Frequently asked questions
Why is the investment rate higher than the discount rate?
The discount rate divides the discount by the larger face value and uses a 360-day year. The investment rate divides by the smaller price and uses a 365- or 366-day year. Both differences make the investment rate higher.
Can the purchase price be higher than the face value?
Not for a bill bought at auction: bills are sold at or below face value. The calculator rejects a price above face value.
How many days should I enter for a 26-week bill?
Usually 182 days, though the exact number depends on the issue and maturity dates. Use the dates in your TreasuryDirect account or brokerage confirmation for precision.
Why does the result change when I enter an issue date?
If the year after the issue date includes February 29, the Treasury’s formula uses a 366-day year for the investment rate. The issue date also lets the calculator show the maturity date.
Does this calculator store what I type?
No. All calculations happen in your browser and nothing you enter is sent to our server.
Related guides
- How Treasury Bill Yield Is Calculated: the discount rate and investment rate formulas, step by step.
- How Treasury Bill Maturity Works: bill terms, issue and maturity dates, counting days and rolling bills over.
- Treasury Rates vs. Savings Account Rates: how a T-bill compares with a high-yield savings account.
Sources
- TreasuryDirect, Treasury Bills, including the published pricing and yield formulas.
- Our methodology and guide to T-bill yields.