Investing & Income
Treasury Bill Calculator
Work out a Treasury bill’s yield from its price and days to maturity: discount rate, bond-equivalent (investment) yield and annual yield, with the formulas.
Annual yield
4.13%
compounded, comparable with a savings account
Profit
$200
2.04% over the period
Investment rate
4.09%
US, as TreasuryDirect shows it
Discount rate
3.96%
US auction quote
Simple yield, 360 days
4.04%
how Spain's Letras and France's BTF are quoted
You pay $9,800 today and receive $10,000 in 182 days: a profit of $200, or 2.04% over the period.
Quoted the US way, that is a 3.96% discount rate and a 4.09% investment rate. Quoted the way Spain's Letras del Tesoro and France's BTF are, it is 4.04%.
Reinvested at the same rate for a full year, it would earn 4.13%: the figure to compare with a savings account's annual yield.
Your numbers
US bills: 4 weeks = 28 days, 13 weeks = 91, 26 weeks = 182, 52 weeks = 364.
Same bill, four ways to quote its yield
- Discount rate (US auction quote)
- 3.96%
- Simple yield, 360-day year (Letras, BTF)
- 4.04%
- Investment rate (TreasuryDirect)
- 4.09%
- Annual yield, compounded
- 4.13%
The discount rate divides the profit by the face value, the others by the price you pay. Counting a 360-day year makes a rate look smaller than counting 365, and compounding over a year adds a little more.
The four yield formulas
Investment rate = (Face value − Price) ÷ Price × 365 ÷ Days
Discount rate = (Face value − Price) ÷ Face value × 360 ÷ Days. Simple yield, 360 days = (Face value − Price) ÷ Price × 360 ÷ Days. Annual yield = (Face value ÷ Price)^(365 ÷ Days) − 1.
The investment rate above applies to bills of up to 182 days. For longer bills, such as the 52-week bill, the US Treasury solves a quadratic equation that assumes a coupon halfway through, so that a 52-week bill compares fairly with notes paying interest twice a year. The calculator uses that same method (31 CFR Part 356, Appendix B) with a 365-day year.
How Treasury bills work
A Treasury bill pays no interest along the way. You buy it below its face value and the government repays the full face value on the maturity date; the difference is your return. Because the return comes from the price alone, the same bill can be described by several rates, depending on what the profit is divided by and how many days a year is counted as.
Example: a US 26-week bill. At a 4.00% discount rate, a $10,000 bill costs $9,797.78 and repays $10,000 after 182 days, a profit of $202.22. TreasuryDirect shows an investment rate of 4.14%, the simple 360-day yield is 4.08%, and reinvested at the same rate for a year it would earn 4.18%.
Example: a 12-month Spanish Letra. A Letra of 364 days awarded at 2.5% costs about 97.53% of its face value. Its compounded annual yield is 2.53%, the figure to compare with a deposit’s annual rate.
Bills are among the safest places for money you will need within a year, but their rate is fixed only until they mature: rolling into new bills means accepting whatever the next auction pays. For longer horizons, the bond yield calculator handles bonds that pay coupons, and the real return calculator shows what is left after inflation.
Treasury Bill FAQ
Why does my T-bill show two different rates?+
US Treasury auctions announce a discount rate, which divides the profit by the face value and counts a 360-day year. TreasuryDirect also shows an investment rate, which divides the profit by the price you actually paid and counts a 365-day year. The investment rate is always the higher of the two and is the one to compare with other investments.
How do I turn a quoted rate into a price?+
For a US bill quoted at a discount rate: price = face value × (1 − discount rate × days ÷ 360). For a bill quoted at a simple yield, as Spain’s Letras del Tesoro are: price = face value ÷ (1 + yield × days ÷ 360). Enter the result as the purchase price and the calculator shows the other conventions.
How are Spain’s Letras del Tesoro quoted?+
Letras with up to a year to run are quoted at a simple interest rate on a 360-day year, the “simple yield, 360 days” figure here. The average rate published after each auction already uses that convention, so it is a little lower than the compounded annual yield for the same Letra.
Is the annual yield the same as a savings account’s APY?+
It is built the same way: the return reinvested at the same rate until a full year has passed, so it is the fairest figure to compare a bill with a savings account or a deposit. In reality you would roll into a new bill at whatever rate the next auction offers.
Are T-bill returns taxed?+
In the US, the difference between the price and the face value is interest for tax purposes: it is subject to federal income tax but exempt from state and local income taxes. In other countries the rules differ, so check with your tax authority. The yields here are before tax.
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Educational tool, not advice. This calculator illustrates a standard formula using the numbers you enter. It does not account for your full financial picture, taxes, or local market conditions, and it is not a recommendation to buy, sell, or hold any asset. Speak with a licensed professional before making investment decisions.
See our full disclaimer and how we calculate.
Last reviewed 2026-11-10 by the Yield Analyst team