π Bond-Equivalent Yield Calculator
T-bill quotes translated to true yield.
Bond-equivalent yield (annualized, 365-day)
Estimates for planning only, not financial advice.
Bond-equivalent yield restates a short-term discount return on the same basis as bond yields, so T-bills can be compared to everything else. A 182-day T-bill bought at 97.80 per 100 of face earns $2.20 over 182 days; the BEY is ($2.20 / $97.80) x (365 / 182) = 4.511 percent. The quoted bank discount rate on the same bill is only 4.352 percent, because it divides by face value instead of price and uses a 360-day year. Same bill, two numbers; BEY is the honest one.
How to Use This Calculator
Enter the face value, the price you pay, and days to maturity. The calculator returns the BEY, the holding-period return, the bank discount rate for comparison, and the dollar profit on the face amount.
Enter face value (usually 100 for quotes) and your purchase price. Secondary-market buyers use the actual traded price.
Enter days to maturity: 91, 182, or 364 for standard bills, or the exact days for secondary purchases.
Compare the BEY to alternatives on the same basis: money-market SEC yields, CD APYs, and Treasury note yields. For compounded comparisons, use our APY calculator.
The Formulas
The two differences between BEY and the discount rate are both in BEY's favor economically: dividing by price (money actually invested) instead of face, and annualizing over 365 real days instead of a 360-day quoting year. Each difference is small; together they add about 0.16 points on our example bill, which is real money at institutional scale and a useful edge in personal comparisons.
Worked Example: 182-Day Bill at 97.80
Face: $100. Price: $97.80. Days: 182. Discount: $2.20. Holding-period return: $2.20 / $97.80 = 2.2495%. Annualization factor: 365 / 182 = 2.0055. BEY: 2.2495% x 2.0055 = 4.511%. Bank discount rate: ($2.20 / $100) x (360 / 182) = 2.20% x 1.9780 = 4.352%.
Dollar view: $10,000 face bought for $9,780 earns $220 over 182 days. Annualized at BEY, that is the equivalent of a 4.511% bond yield. A money-market fund quoting 4.45% and this bill at 4.511% BEY: the bill wins on yield, and its state-tax exemption widens the lead further for filers in high-tax states.
Quoting Conventions Compared
| Instrument | Quoted as | Convert via |
|---|---|---|
| T-bills (auction) | Discount rate + investment rate | Investment rate is the BEY |
| Commercial paper | Discount rate | BEY formula |
| CDs | APY | Comparable to BEY directly |
| Treasury notes | Yield to maturity | Same 365-day basis as BEY |
TreasuryDirect does the conversion for you by publishing the investment rate alongside the discount rate; in secondary markets and for commercial paper, this calculator does it. Never compare a discount rate to an APY or a YTM without converting: the quoting gap is not a yield gap.
Using BEY in Cash Decisions
For cash you will need within a year, rank options by after-tax BEY-equivalent yield: T-bill BEY adjusted for the state exemption, money-fund SEC yield adjusted for its taxable share, CD APY with early-withdrawal penalties noted. The winner is usually the T-bill in high-tax states and a money fund or CD elsewhere, but the margin is thin enough that convenience and minimums often decide.
Ladder bills (4, 8, 13, 17, 26, 52 weeks) to keep cash rolling at current rates without timing risk, and remember BEY is pre-tax federal: the after-tax comparison is what spends. Our CD calculator models the bank alternative fully, and the bond calculator prices the longer-term Treasury notes the bills roll into when your horizon extends.
BEY in Practice: Auctions and Ladders
Treasury auctions publish both the discount rate and the investment rate; the investment rate is the BEY, and it is the number to compare against your alternatives. Noncompetitive bidders get the auction's market-clearing rate, which is why TreasuryDirect works for individuals: you accept the market price without needing to bid. Auction schedules are weekly for bills, so cash never waits long for deployment.
Laddering turns BEY comparisons into a system: buy 4, 13, and 26-week bills in rotation so something matures every month at the current rate. When the Fed cuts, the ladder's average yield falls gradually instead of dropping all at once; when it hikes, new rungs capture the higher rates. Compare each rung's BEY to money-market and CD alternatives net of state tax, and let the after-tax winner take the cash. The ladder removes timing decisions, which is where most cash investors lose.
One more comparison: tax-equivalent yield translates tax-exempt returns into taxable terms, the mirror image of BEY's quoting translation. A 3 percent tax-exempt yield at a 24 percent federal bracket equals 3.95 percent taxable, which often beats a T-bill's BEY for high-bracket investors. Run both translations before choosing: BEY standardizes the quoting, tax-equivalence standardizes the tax treatment, and the winner is the one that leaves the most after tax.
Estimates for planning only, not financial advice.
Frequently Asked Questions
What is bond-equivalent yield?
The annualized yield on a short-term discount investment restated on a bond-like basis: BEY = ((face - price) / price) x (365 / days). A 182-day T-bill at 97.80 per 100 of face has a BEY of 4.511%. It lets you compare T-bills against coupon bonds and other yields apples to apples.
What is the bond-equivalent yield formula?
BEY = (discount / price) x (365 / days to maturity), where discount = face value - price. For a $100 T-bill priced at $97.80 with 182 days left: ($2.20 / $97.80) x (365/182) = 2.2495% x 2.0055 = 4.511%. The first term is the holding-period return; the second annualizes it on a 365-day year.
How is BEY different from the discount rate?
The bank discount rate uses face value in the denominator and a 360-day year: discount rate = (discount / face) x (360 / days). Our T-bill's discount rate is ($2.20/$100) x (360/182) = 4.352%, lower than the 4.511% BEY. BEY is the economically honest number: return on money actually invested, over a real year. Quotes use the discount rate; decisions should use BEY.
Why 365 days and not 360?
Convention with an economic logic: bond yields annualize over actual calendar days, so BEY uses 365 to match. The 360-day bank year is a quoting relic that understates true yield by about 1.4% relatively (365/360). When comparing a T-bill to a bond fund's SEC yield, BEY's 365-day basis is the comparable one.
When do I need bond-equivalent yield?
Whenever comparing short-term instruments quoted differently: T-bills (discount rate) vs commercial paper vs CDs vs Treasury notes (yield to maturity). Without conversion, the quoting conventions make the comparison meaningless. BEY is the common denominator for anything under a year.
Does BEY account for compounding?
No: BEY is a simple annualized rate, not a compounded one. For periods under a year the difference is tiny, which is why the market accepts the simple form. For true effective annual yield with reinvestment, compute (1 + holding return)^(365/days) - 1, which runs slightly higher. Our <a href="/finance/apy">APY calculator</a> handles the compounded version.
What is the T-bill investment rate?
Another name for BEY in Treasury auctions: the "investment rate" on TreasuryDirect is the bond-equivalent yield of the bill. When auction results show a 4.35% discount rate and a 4.51% investment rate, the second number is the BEY, and it is the one comparable to other investments.
How do taxes affect T-bill yields?
T-bill interest is exempt from state and local income tax but subject to federal tax. In a high-tax state, that exemption is worth real money: a 4.51% BEY at a 9% state rate beats a fully taxable 4.51% CD by about 0.41 points after tax. Adjust the comparison for your state bracket.
BEY vs money market fund yield?
Money funds quote 7-day SEC yields, already annualized on a bond-equivalent-ish basis, so they compare directly to T-bill BEYs. The choice then turns on taxes (T-bills' state exemption vs the fund's composition), minimums, and liquidity, not on quoting math.
Can BEY be negative?
Yes, when the price exceeds face (negative discount): investors paying $100.10 for $100 of bill get a negative BEY. It happens in flight-to-safety episodes when return of capital beats return on capital. The formula handles it naturally; the economics are just unusual.