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Bond Equivalent Yield Calculator
Bond Equivalent Yield Calculator
Bond Equivalent Yield
6.11%
Yield Analysis
The $150 discount annualizes to a 6.11% bond-equivalent yield over 91 days, well above the Treasury-bill-style discount yield of 5.93% that banks quote on a 360-day basis. The BEY figure is the right one to compare against coupon-bearing bonds and savings products quoted on a 365-day, annual basis.
*The bond equivalent yield converts a discount into an annual figure for comparison only; actual realized yield depends on reinvestment and holding period. Educational only, not investment advice.
Comparing Discount Instruments on a Level Field
The bond equivalent yield (BEY) converts the return on a discount instrument — something sold below face value and redeemed at par — into an annual percentage rate that can be compared directly with coupon-bearing bonds, CDs, and savings products. Treasury bills, commercial paper, and short-term municipal notes do not pay interest; they pay their investor by maturing at more than the purchase price. That discount is not an annual rate, and the time to maturity may be 28 days or 182 days, so quoting a raw return is not comparable across instruments. For US investors the BEY matters because the Treasury market itself quotes bills on a confusing basis. Bank discount yield, the figure you see in Treasury auction results, understates the true return by using the face value as the denominator and a 360-day year. The bond equivalent yield corrects both distortions: it uses the actual purchase price and a 365-day year, giving the number that corresponds to what a coupon-bearing bond would quote. When you are deciding between a 91-day Treasury bill, a money market fund, and a 6-month CD, the BEY is the yardstick that makes all three speak the same language.
Annualizing a Discount Correctly
The core return on a discount instrument is simple: the dollar discount (Face Value minus Purchase Price) divided by the price actually paid. A $10,000 bill bought for $9,850 returns $150, a 1.52% holding-period gain. The BEY then scales that holding-period return to a full year by multiplying by 365 divided by the days to maturity: BEY = (Face − Price) ÷ Price × (365 / Days). The contrast with the bank discount yield shows why the choice of formula matters. Bankers divide the discount by face value instead of price, and use a 360-day year, so the same bill quotes a lower rate. On the $10,000 example held for 91 days, the bank discount yield reads about 5.90% while the BEY reads about 6.08% — same bill, two quotes. This tool also computes the effective annual yield, which compounds the holding-period return across how many times that period fits in a year, the fairest measure for multi-period reinvestment. For anything quoted on a discount basis, always convert to BEY before comparing it to coupon securities quoted in the annual convention.
Expert Insights
Never Compare a Discount Quote to a Coupon Quote
A money fund's 5.2% and a T-bill's 5.0% auction high rate are not apples-to-apples: one is a 365-day annual figure, the other is a 360-day discount-basis quote. The T-bill's BEY will typically quote closer to 5.2% or more. Always convert to the same convention before choosing where cash parks.
Shortening the Maturity Amplifies Yield Errors
The annualization factor 365/days multiplies everything — including any pricing mistake. On a 28-day instrument, a $10 price difference on $10,000 shifts the BEY by more than a full percentage point. This is why short instruments demand precise pricing, and why BEY can look deceptively volatile for bills under a month.
BEY Ignores Reinvestment Risk
The BEY assumes you can reinvest the proceeds at the same annualized rate for the rest of the year. In a falling-rate environment that assumption fails. For cash management, pair the BEY with the direction of short-term rates; a slightly lower rate on a longer instrument can beat a high bill rate you cannot reinvest.
Actionable Tips
- 1
Convert Every Short-Term Quote Before Buying
When you see a Treasury auction quote or a CD advertised on a 360-day basis, run it through this calculator with the exact purchase price and days to maturity. Compare the resulting BEY to your money-market fund's 7-day yield. The highest BEY is not always the best after-tax or after-reinvestment return.
- 2
Check the Purchase Price at Auction
For competitive T-bill bids, the purchase price depends on the accepted discount rate, so work backward from the rate to find the exact dollars paid. Plug that price in here rather than using the headline rate. A small error in the denominator compounds through the annualization.
- 3
Mind the Tax Treatment Too
Treasury discount income is federally taxed but exempt from state and local tax, while CD interest is fully taxable. Two instruments with identical BEYs can differ by a meaningful after-tax margin in high-tax states. Factor your state rate into the comparison whenever a Treasury is one of the options.
Real-World Examples
Priya Switched Her Cash Sweep After One Calculation
Priya's brokerage swept cash into a money fund at 4.1%. She priced a 13-week T-bill at auction and ran the BEY: 4.45%, with no state tax. Over $50,000 the difference was modest but risk-free, so she laddered bills every month and kept only one month's expenses in the fund.
Tom Caught a Misleading CD Advertisement
A bank advertised a 9-month CD at 5.7% 'discount yield'. Tom converted it with this calculator and found the BEY was actually 5.2% — the bank had quoted the discount basis. He compared it against a 9-month Treasury at 5.4% BEY and chose the Treasury, netting more after-tax income.
Dev Understood Why His Bill Yield Looked Huge
Dev bought a 14-day bill and saw the BEY read over 7%, far above everything else. He realized the annualization factor of roughly 26 magnified a tiny two-week return into a dramatic annual figure. He learned to read ultra-short BEYs as arithmetic, not a durable income rate, and sized the position as a parking spot rather than a return.
Glossary of Terms
- Bond Equivalent Yield (BEY)
- A discount instrument's return annualized on a 365-day basis using the purchase price, making it comparable to coupon bond yields.
- Bank Discount Yield
- The quote convention used for Treasury bills: discount divided by face value on a 360-day year; understates true return.
- Effective Annual Yield
- The true annualized return when a short-period gain is assumed to be compounded for the full year.
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Ivy Sinclair-Wren
Financial Chaos Analyst
Ivy Sinclair-Wren is a Financial Chaos Analyst covering investing, AI, wealth psychology, and the emotional consequences of opening finance apps during market crashes. Based in Melbourne, she specializes in demystifying the US tax code and helping users navigate the intersection of spreadsheet logic and human irrationality.