This bond equivalent yield calculator converts a Treasury bill’s quoted discount yield into the bond equivalent yield — the true annualized return on the price you actually paid — so T-bills can be compared honestly with notes, bonds and CDs.

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The Quote Is Rigged — Politely, By Convention

Treasury bills don't pay coupons; you buy them at a discount and receive face value at maturity. The market quotes them on a discount yield basis: (FV − P)/FV × (360/days) — a formula with two deliberate understatements baked in since the era of hand calculation. It divides your profit by the face value (larger than what you paid, shrinking the yield) and pretends the year has 360 days (shrinking it again). The bond equivalent yield undoes both: BEY = ((FV − P)/P) × (365/days) — return on YOUR money, over a real year. The defaults: a $10,000 bill bought at $9,800 with 182 days to run earns a holding-period return of 200/9,800 = 2.0408%, which annualizes to a BEY of 4.09% — versus the 3.96% the discount convention would quote for the identical bill. Thirteen basis points of pure definitional fog, on the safest asset in the world.

BEY exists so comparisons can be honest. A coupon bond's yield to maturity is computed on price paid over a 365-day year (with compounding nuances), so a bill's discount yield and a note's YTM are apples and filing cabinets until the bill is converted. Money-market desks, Treasury auction results and the financial press all publish BEY (the Treasury's "investment rate") for exactly this reason. One more refinement for completeness: for bills longer than half a year, the official BEY formula adds a compounding adjustment (treating the bill as if it paid a semi-annual coupon), which this calculator's simple form approximates closely; the difference is a few basis points and matters to traders, not to comparisons. The broader lesson travels: quoted yields are conventions, not facts — always ask on what basis, over what year, on which denominator, before ranking two instruments by a decimal.

Worked Examples (Verified)

  • Defaults: FV $10,000, price $9,800, 182 days → BEY 4.09% vs discount yield 3.96%.
  • 13-week bill: FV $10,000, price $9,900, 91 days → HPY 1.0101% → BEY 4.05%; discount yield 3.96%.
  • 4-week bill: FV $10,000, price $9,970, 28 days → BEY 3.92%; discount yield 3.87%.
  • Deep discount: FV $10,000, price $9,500, 364 days → BEY 5.28% vs discount yield 4.95% — the gap grows with the discount.

BEY Discipline

  • Never compare a discount yield directly with a YTM or APY — convert to BEY (or APY) first, or the bill loses a race it actually won.
  • BEY here is a simple (non-compounded) annualization: APY of the same bill is slightly higher — (1 + HPY)^(365/days) − 1.
  • For bills over 182 days the official Treasury investment-rate formula includes a semi-annual compounding adjustment; expect differences of a few bps from this calculator on long bills.
  • The denominator is the whole story: discount yield divides by face, BEY by price. When someone quotes you a yield, the first question is "divided by what?"
  • Actual/360 lives on in money markets (commercial paper, LIBOR-era conventions) — recognize the convention rather than assuming error.

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Frequently Asked Questions

How do you calculate bond equivalent yield?

BEY = ((face value − price) ÷ price) × (365 ÷ days to maturity). For a $10,000 bill at $9,800 with 182 days left: (200/9,800) × (365/182) = 4.09%. The formula takes your actual holding-period return on the price paid and annualizes it over a true 365-day year. This calculator also shows the conventional discount yield alongside, so you can see exactly how much the quoting convention understates the same investment.

Why is BEY higher than the discount yield?

Two corrections, both in your favor. The discount yield divides the profit by face value ($10,000) rather than by your price ($9,800), shrinking the return; and it annualizes over 360 days rather than 365, shrinking it again. BEY fixes the denominator to the money you actually invested and the year to the calendar's. The longer the maturity and the deeper the discount, the wider the gap — at 364 days and a $500 discount it reaches 33 basis points in the worked examples above.

What is the difference between BEY and yield to maturity?

YTM is the internal rate of return of a coupon bond's full cash-flow stream — coupons plus principal, with compounding. BEY is a simpler animal: a single discount cash flow annualized without compounding (in its standard short-bill form). For comparing a T-bill against a note or CD at a glance, BEY is the intended bridge — it puts the bill on the same "return on price, per year" footing. For precise total-return work on coupon bonds, YTM (or APY-style effective yield) is the rigorous measure.

Why do T-bills use a 360-day year at all?

History and arithmetic convenience: the bank discount basis dates to hand-calculated markets where 360 (divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12…) made mental math easy, and the convention fossilized into auction rules and textbooks. Money markets still run several actual/360 conventions today. It is not a conspiracy — but it is a systematic understatement of investor return, which is precisely why regulators require the BEY ("investment rate") to be published next to auction results.

Is BEY the same as APY?

No — APY compounds. BEY annualizes the holding-period return linearly (× 365/days); APY raises it to a power ((1 + HPY)^(365/days) − 1), crediting interest-on-interest. For the default bill: BEY 4.09%, APY ≈ 4.13%. When comparing a T-bill with a bank CD quoted in APY, convert the bill to APY for a fair fight, or the CD to BEY. The differences are small at short maturities and low rates — and systematically in compounding's favor.

Does BEY apply to other discount instruments?

Yes — commercial paper, agency discount notes and banker's acceptances are all quoted on discount bases and all convert the same way, because the structure (pay P now, receive FV at maturity, nothing between) is identical. The formula only needs price, face and days. What changes across instruments is credit risk, not arithmetic — a 4.09% BEY on a T-bill and 4.09% on commercial paper are equal yields on very different promises, and the yield conversion deliberately says nothing about that gap.

What about bills with more than six months to maturity?

The Treasury's official investment rate for bills over 182 days uses a two-part formula that assumes one semi-annual compounding — as if the bill paid a coupon halfway. The simple BEY on this page will differ by only a few basis points (the official figure runs slightly lower), which is immaterial for comparisons but worth knowing if you're reconciling against TreasuryDirect to the decimal. For bills of 182 days or less, the simple formula IS the official one.

Is this bond equivalent yield calculator free?

Yes — free, instant, no sign-up. Enter face value, price and days to maturity for the bond equivalent yield and the quoted discount yield side by side.