How to Calculate Treasury Bill Yield: Discount, BEY, and EAY

To calculate a Treasury bill yield, you need three numbers — the bill’s face value, the price you paid, and the days from settlement to maturity — and then you pick one of three formulas depending on what you want the answer to tell you. The bank discount yield matches what dealers and the Treasury quote. The bond equivalent yield lets you compare a T-bill to a CD or corporate bond. The effective annual yield adds compounding. Same bill, three different percentages, all correct in their own frame.

The Three Numbers You Need

Every formula below runs on the same inputs. Pull them once and reuse them.

  • Face value. What the Treasury pays you at maturity. T-bills are sold in $100 increments, so this is usually $1,000, $10,000, or another round figure.1TreasuryDirect. Treasury Bills
  • Purchase price. What you actually paid. For a discount bill this is less than face value. It appears on your TreasuryDirect dashboard or your broker’s trade confirmation. Use the dollar price, not the quoted discount rate.
  • Days to maturity. Calendar days from settlement to the maturity date. Current T-bill terms are 4, 6, 8, 13, 17, 26, and 52 weeks.1TreasuryDirect. Treasury Bills

A worked example runs through the whole article: a $10,000 T-bill bought for $9,800 with 90 days to maturity. The dollar discount is $200.

Bank Discount Yield

This is the yield quoted in financial news and reported by the Treasury as the “high rate” at each auction.2eCFR. 31 CFR Part 356 – Sale and Issue of Marketable Book-Entry Treasury Bills, Notes, and Bonds It uses a 360-day year and divides by face value rather than by what you paid.

  1. Subtract the purchase price from the face value to get the dollar discount.
  2. Divide the discount by the face value.
  3. Multiply by 360 divided by days to maturity.

For the example: $200 ÷ $10,000 = 0.02. Then 0.02 × (360 ÷ 90) = 0.02 × 4 = 0.08, or 8%.

That 8% understates your real return. You didn’t invest $10,000; you invested $9,800. And a year is 365 days, not 360. The bank discount number is useful mainly because it is the convention everyone else quotes, so you need it to match what you see on auction results and dealer screens.

Bond Equivalent Yield

Also called the investment rate or coupon equivalent yield. This is the number to use when comparing a T-bill against any other fixed-income product. It divides by the price you actually paid and uses a 365-day year.

Bills of 182 Days or Fewer

This covers the 4-, 6-, 8-, 13-, 17-, and 26-week bills.

  1. Subtract the purchase price from the face value to get the dollar profit.
  2. Divide the profit by the purchase price.
  3. Multiply by 365 divided by days to maturity.

For the example: $200 ÷ $9,800 ≈ 0.02041. Then 0.02041 × (365 ÷ 90) ≈ 0.02041 × 4.056 ≈ 0.0828, or 8.28%.

That’s higher than the 8% bank discount yield for two reasons working in the same direction: a smaller denominator (what you invested) and a longer year (365 days). The Treasury publishes this figure as the “investment rate” alongside every auction. As a rough reference point, in early 2026 the 13-week investment rate ran around 3.69% and the 52-week around 3.62%.3U.S. Department of the Treasury. Daily Treasury Bill Rates

The 52-Week Bill Is Different

For bills with more than 182 days to maturity, the simple formula above gives a slightly wrong answer. A comparable coupon bond would pay interest semiannually during the holding period, and the Treasury’s official formula (Appendix B of 31 CFR Part 356) solves a quadratic that builds in that semiannual convention.4eCFR. Appendix B to 31 CFR Part 356 – Formulas and Tables You don’t need to work through it by hand. Use the investment rate the Treasury publishes with the auction, or a calculator that applies the semiannual adjustment.

Effective Annual Yield

This one asks a different question: if you kept rolling the money into an identical T-bill every time one matured, what would a full year’s return look like? It adds compounding to the picture the bond equivalent yield already gives you.

  1. Divide the dollar profit by the purchase price. That’s your holding-period return.
  2. Add 1 to it. That’s your growth factor.
  3. Raise the growth factor to the power of 365 ÷ days to maturity.
  4. Subtract 1.

For the example: holding-period return is 0.02041, growth factor is 1.02041, and 1.02041 raised to the 4.056 power is roughly 1.0854. Subtract 1, and you get about 8.54%.

The effective annual yield is always the highest of the three measures on the same bill. The gap widens as the term shortens, because a 4-week bill compounds about 13 times a year while a 52-week bill compounds only once. Treat it as a theoretical ceiling. Actual reinvestment happens at whatever rate the next auction produces, and that rate moves.

Which Yield to Use

Match the formula to the question you’re trying to answer.

  • Verifying what the Treasury or a dealer quoted you: bank discount yield.
  • Comparing a T-bill against a CD, corporate bond, or money market fund: bond equivalent yield.
  • Estimating a full-year return assuming continuous reinvestment: effective annual yield.

If you bought at auction and just want to check the math on your confirmation, the Treasury’s published auction results show the high rate, the investment rate, and the price per $100 of face value.5TreasuryDirect. Announcements, Data and Results Plug the price into the formulas above and you should reproduce the published rates.

The After-Tax Adjustment That Changes the Comparison

T-bill interest is exempt from state and local income tax under federal law.6Office of the Law Revision Counsel. 31 USC 3124 – Exemption From Taxation Federal income tax still applies to the discount, and you generally report it in the year the bill matures, not the year you bought it.7Internal Revenue Service. Publication 550 – Investment Income and Expenses The amount shows up in box 3 of Form 1099-INT, the box reserved for interest on Treasury obligations.8Internal Revenue Service. Instructions for Forms 1099-INT and 1099-OID

That state exemption means comparing a T-bill’s stated yield against a CD’s stated yield understates the T-bill. To make an apples-to-apples comparison, gross up the T-bill’s bond equivalent yield by your state rate: divide it by one minus your state income tax rate written as a decimal.

At a 3.69% bond equivalent yield and a 6% state tax rate, that’s 3.69% ÷ (1 − 0.06) = 3.69% ÷ 0.94 ≈ 3.93%. A CD would need to yield at least 3.93% to match the T-bill after tax. In states with no individual income tax, the adjustment is zero and the stated yields compare directly. In high-tax states, the gap can matter enough to flip the decision.