Treasury bills don’t pay interest the way a savings account does. You buy a bill for less than its face value and receive the full face value when it matures. Your earnings are the difference. Turning that discount into an annual yield can be done in more than one way, and the Treasury itself quotes two: the discount rate and the investment rate. Knowing the difference keeps you from comparing apples with oranges.
Step 1: the discount
The discount is simply face value minus price. If you pay $9,900 for a $10,000 bill, the discount is $100. Over the bill’s term, your return is $100 ÷ $9,900 = 1.01%.
Step 2a: the discount rate (bank discount yield)
Discount rate = (Face − Price) ÷ Face × 360 ÷ Days
The discount rate expresses the discount as a percentage of the face value and annualizes it over a 360-day year, a convention from money markets. For a 91-day bill bought at $9,900 per $10,000: $100 ÷ $10,000 × 360 ÷ 91 = 3.956%.
Bill auction results are quoted with a discount rate, and the auction price is calculated from it:
Price = Face × (1 − Discount rate × Days ÷ 360)
Step 2b: the investment rate (coupon-equivalent yield)
Investment rate = (Face − Price) ÷ Price × 365 ÷ Days
The investment rate expresses the discount as a percentage of the price you paid and annualizes it over a 365-day year (366 when the year after the issue date contains February 29). For the same bill: $100 ÷ $9,900 × 365 ÷ 91 = 4.052%.
This is the rate to use when comparing a bill with Treasury notes, CDs or other investments, because it measures return on the money you actually put in over a real calendar year.
Why the two rates differ
- The discount rate divides by face value, which is larger than the price, so it gives a smaller percentage.
- The discount rate uses a 360-day year, the investment rate a 365- or 366-day year.
Both effects push the discount rate lower, so for the same bill it is always below the investment rate. The gap grows as rates rise and terms lengthen.
Bills longer than half a year
For bills that mature in more than half a year, such as 52-week bills, the Treasury calculates the investment rate with a formula that reflects the semiannual coupon a comparable note would pay:
i = [ −2t/y + 2 × √( (t/y)² − (2t/y − 1)(1 − 100/P) ) ] ÷ (2t/y − 1)
Here t is the days to maturity, y the days in the year and P the price per $100 of face value. You don’t need to work this out by hand: our Treasury Bill Calculator chooses the right formula and shows its steps.
A third number: effective annual yield
Bank accounts often quote an annual percentage yield (APY) that assumes interest is reinvested. To compare like with like, you can compound a bill’s term return over a year: (Face ÷ Price)365/Days − 1. For our example: (10,000 ÷ 9,900)365/91 − 1 ≈ 4.11%. This assumes you could reinvest at the same rate, which is not guaranteed.
And the rate on our rates dashboard?
The daily 3-month Treasury rate on this site is the Treasury’s par yield curve rate on a bond-equivalent basis, calculated from end-of-day market prices. It is closest in concept to the investment rate, but it is not the result of a particular auction.
Summary
| Discount rate | Investment rate | |
|---|---|---|
| Based on | Face value | Price paid |
| Year length | 360 days | 365 or 366 days |
| Used for | Auction quotes, pricing | Comparing with other investments |
| Relative size | Lower | Higher |
To see how bill terms, issue dates and maturity work in practice, read How Treasury Bill Maturity Works, or run your own numbers in the Treasury Bill Calculator.
Example figures in this article are illustrations, not current market rates. Formulas follow those published by TreasuryDirect.