Bond Equivalent Yield (BEY
Short-term Treasury bills are quoted on a Bank Discount Yield (BDY) basis using a 360-day year.
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📐 Formula
💡 Practical Example
91-day Treasury Bill purchased at $98.50 per $100 face value: Dollar Gain = $1.50. BEY = × = 0.015228 × 4.01099 = 6.108%. Bank Discount Yield = × = 5.934%.
📖 About Bond Equivalent Yield (BEY
Short-term Treasury bills are quoted on a Bank Discount Yield (BDY) basis using a 360-day year. Converting to a Bond Equivalent Yield (BEY) uses a 365-day year and actual purchase price, allowing direct comparison with semi-annual coupon bonds.
To use the Bond Equivalent Yield (BEY) & T-Bill Converter, enter your Discount Purchase Price, Face / Par Value, Days to Maturity. The calculator instantly computes Bond Equivalent Yield (BEY - 365 Days), Bank Discount Yield (360 Days) and more. Results update in real time as you change any input — no submit button needed.
How to Use This Calculator
Enter your Discount Purchase Price (e.g. 98.50 in ), Face / Par Value (e.g. 100 in ), and Days to Maturity (e.g. 91 in days). Results update instantly as you type — adjust any value to compare scenarios.
The Formula
Bond Equivalent Yield BEY (%) = [ (Face Value - Purchase Price) ÷ Purchase Price ] × (365 ÷ Days to Maturity) × 100
Bank Discount Yield BDY (%) = [ (Face Value - Purchase Price) ÷ Face Value ] × (360 ÷ Days to Maturity) × 100
Worked Example
91-day Treasury Bill purchased at 98.50 per 100 face value:
Dollar Gain = 1.
50.
BEY = = 0.015228 × 4.01099 = 6.108%.
Bank Discount Yield = = 5.934%.
Understanding Your Result
For financial decisions, validate your result against your specific tax situation, current interest rate environment, and applicable regulations — these change frequently and vary by jurisdiction. A calculated estimate is a useful starting point; for decisions involving significant capital (more than one month's income), consult a certified financial planner (CFP) or CPA. Financial projections beyond 3–5 years carry increasing uncertainty — model a conservative, base, and optimistic scenario to understand the range of outcomes.
💡 Mathematical Rigor & Applied Context
- This calculator applies exact mathematical definitions following conventions established by NIST and international standards bodies.
- Rounding errors accumulate across multi-step calculations. For precision-critical work, maintain extra significant figures through all intermediate steps.
- Many mathematical concepts have multiple valid formulations — if a result seems unexpected, verify which convention or definition applies to your context.
- Dimensional analysis (unit tracking) is the fastest way to catch formula errors. Every term in an equation must have consistent, compatible units.
- Numerical methods used in digital calculators introduce floating-point precision limits (~15 significant digits for IEEE 754 double precision).
- For statistical and probabilistic calculations, always specify whether you are working with population parameters or sample statistics — formulas differ.
- Visualizing a problem geometrically or testing with known boundary values (zero, infinity, negative) reveals hidden errors faster than algebraic checking.
- When in doubt, validate your result against a simplified hand calculation or a published worked example from a textbook or standards document.
Results are for informational and educational purposes only. Always verify critical decisions with a qualified professional.