Treasury Bill Calculator
The price of a US Treasury bill from its discount rate, or its discount rate and investment rate from the price, by the formulas in the Treasury’s auction rules.
Result
Price: $977.25
By the Treasury’s published formulas, on the rate or price you enter. Auction prices are rounded to six decimals per 100.
- Investment rate
- 4.6687%
- Interest earned (the discount)
- $22.75
- Discount rate
- 4.5%
- Price per 100 of face value
- 97.725
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Results are arithmetic on the returns, rates and horizons you enter, not a forecast and not investment, tax or retirement advice. The site supplies no expected return, inflation rate, contribution limit, tax rate or withdrawal rate. Real returns vary from year to year, and fees, taxes and the order of returns all change the outcome. Check anything that matters with a qualified adviser. Read the full disclaimer
How to use the Treasury Bill Calculator
- Enter the bill's face value and the days to maturity, such as 28, 91, 182 or 364.
- Choose whether you know the discount rate or the price, and enter it.
- Read the price or the investment rate, the interest earned, and the other rate for comparison.
The formulas
price per 100 P = 100 × (1 − d × r ÷ 360)discount rate d = (100 − P) ÷ 100 × 360 ÷ rinvestment rate i = (100 − P) ÷ P × y ÷ r (half a year or less)(r ÷ 2y − 0.25) × i² + (r ÷ y) × i + (P − 100) ÷ P = 0 (longer)r is the days to maturity and y the days in the year, 365 or 366. These are the formulas in appendix B to 31 CFR part 356, the rules for Treasury auctions, which TreasuryDirect points to for its pricing.
Interest without a coupon
A bill pays no interest along the way. You buy it below face value and receive the full face value at maturity; the difference is your interest. That is why the price is worked out from a discount rather than a yield.
What the diagram shows
What the bill costs beside what it pays at maturity. The gap between the bars is all the interest the bill earns.
With your numbers
- Price per 100 = 100 × (1 − 4.5% × 182 ÷ 360) = 97.725
- Investment rate = (100 − 97.725) ÷ 97.725 × 365 ÷ 182 = 4.6687%
Quick reference
By the Treasury’s published formulas, on the rate or price you enter. Auction prices are rounded to six decimals per 100.
| Example | Result |
|---|---|
| 1,000, 26 weeks at 4.5% | Price: $977.25 |
| 1,000, 26 weeks at 0.145% | Price: $999.27 |
| 100, 90 days at 7.61% | Price: $98.10 |
| 10,000, 4 weeks at 5% | Price: $9,961.11 |
| 10,000, 52 weeks at 5% | Price: $9,494.44 |
| Bought at 92,265 per 100,000 for 364 days | Investment rate: 8.2373% |
Common questions about the Treasury Bill Calculator
- Why are there two rates?
- The discount rate is how bills are auctioned: the discount as a share of face value, over a 360-day year. It understates what you earn, because you pay less than face value and the year has more than 360 days. The investment rate, also called the coupon-equivalent yield, is the discount as a share of what you paid, over a 365-day year, which makes it comparable with the yield on a note or bond.
- Why does a 52-week bill use a different formula?
- Notes and bonds pay interest twice a year, so their yields assume a coupon at the half-year that can earn interest itself. To stay comparable, the Treasury's formula for a bill longer than half a year includes that effect, which means solving a quadratic. At exactly half a year the two formulas give the same answer, so there is no jump between a 182-day and a 183-day bill.
- How do I get the discount rate?
- It is set at each auction and published by the Treasury. This page supplies none; enter the rate from the auction results or the price you were quoted.
- When should I choose 366 days?
- When the year following the issue date includes 29 February. The Treasury's investment-rate formula then uses 366 days. It changes the investment rate slightly and the price not at all.