Bond Equivalent Yield (BEY) Calculator

Enter your discount yield and days to maturity to calculate the Bond Equivalent Yield (BEY), annual percentage yield, effective price, and holding period return.

Created by Luis GonzalezLast updated: June 16, 2026

How to Use This Calculator

1
Enter Your Bond Details
Input the discount yield (%) and days to maturity for your discount instrument. Common maturities: 91 days (3-month T-bill), 182 days (6-month), 364 days (1-year).
2
Review Results and Insights
The calculator displays three cards — Bond Equivalent Yield, Annual Percentage Yield, and Effective Price — plus an insights panel with holding period return, BEY-vs-discount spread, and the 365-day annualized discount rate.

Example Calculation

A treasurer converts a 180-day T-bill discount yield of 3.5% to its bond equivalent yield for comparison with coupon bonds.

Discount Yield

3.5

Days to Maturity

180

Results

Bond Equivalent Yield

3.6118%

Annual Percentage Yield

3.6444%

Effective Price

$98.2500

Insights card shows holding period return of 1.

Tips

Compare T-Bill Tenors Side by Side

A 91-day T-bill at 5.0% discount yields a BEY of 5.1343%, while a 182-day T-bill at 4.5% yields a BEY of 4.6687%. Even though the 91-day rate is higher, the 182-day bill locks in a 2.3280% holding period return versus just 1.2801% — consider your reinvestment risk.

Understand the Compounding Boost

For a 180-day T-bill at 3.5% discount, the BEY is 3.6118% but the APY is 3.6444% — a 0.0326% compounding bonus. At higher rates (e.g., 5.0% discount on 182 days), the gap widens: BEY of 5.2009% vs APY of 5.2685%, a 0.0676% difference that matters on large positions.

Track the Price You Actually Pay

At 3.5% discount for 180 days, you pay $98.25 per $100 face — a $1.75 gain at maturity. Raise the discount to 5.0% on 182 days and the price drops to $97.4722, netting a $2.5278 gain. Use the effective price to size your cash allocation.

Watch Short-Tenor Sensitivity

A 30-day T-bill at 5.25% discount yields a BEY of 5.3463%, but you only earn 0.4394% over those 30 days. Moving to a 91-day T-bill at 5.0% gets you 1.2801% holding period return — nearly 3x more income, reducing your reinvestment frequency and transaction costs.

The Formula Behind Bond Equivalent Yield

The Bond Equivalent Yield converts a discount yield into an annualized rate comparable to coupon-bearing bonds. The standard formula is:

BEY = (d * t / 360) / (1 - d * t / 360) * (365 / t) * 100

Where d is the discount yield as a decimal and t is days to maturity. The numerator d * t / 360 is the discount factor, and dividing by (1 - discount factor) converts from a face-value basis to a price basis. Multiplying by 365 / t annualizes the result.

For a 180-day T-bill at 3.5% discount: discount factor = 0.0175, holding period return = 0.0175 / 0.9825 = 1.7812%, and BEY = 1.7812% * (365/180) = 3.6118%.

BEY Across Common T-Bill Maturities

Maturity	Discount Yield	BEY	APY	Price per $100	Holding Period Return
91 days	5.00%	5.1343%	5.2002%	$98.7361	1.2801%
182 days	4.50%	4.6687%	4.7232%	$97.7250	2.3280%
182 days	5.00%	5.2009%	5.2685%	$97.4722	2.5933%
364 days	4.50%	4.7800%	4.8371%	$95.4500	4.7669%

💡 To evaluate how T-bill returns compare within a broader portfolio, our Treasury Bill Calculator provides a detailed breakdown of T-bill pricing and returns.

BEY vs APY: When the Difference Matters

BEY uses simple interest while APY assumes semiannual compounding: APY = (1 + BEY/2)^2 - 1. The difference is small at low rates but grows with yield. At 3.5% discount (180 days), the gap is just 0.0326% (3.6118% BEY vs 3.6444% APY). At 5.0% discount (182 days), it widens to 0.0676% (5.2009% vs 5.2685%). For a $10 million T-bill position, that 0.0676% APY premium represents roughly $6,760 in additional annual compounded return — meaningful for institutional treasuries managing cash positions.

💡 For comparing yields across different compounding frequencies, our APY Calculator can convert between nominal rates and effective annual yields.

Practical Application: Comparing Discount Instruments to Coupon Bonds

When a 6-month T-bill is quoted at a 4.5% discount yield, its BEY of 4.6687% is the correct number to compare against a coupon bond yielding 4.75%. The raw discount yield understates the true return because it measures against face value rather than the price you actually pay ($97.7250 per $100 face). The BEY adjustment adds 0.1687 percentage points, which can flip a decision — especially when the credit risk of the coupon bond is higher than a government-backed T-bill.

Frequently Asked Questions

What is Bond Equivalent Yield (BEY) and why does it matter?

BEY converts the discount yield of short-term instruments like T-bills into an annualized rate comparable to coupon bonds. The formula is BEY = (d * t / 360) / (1 - d * t / 360) * (365 / t), where d is the discount rate and t is days to maturity. For example, a 180-day T-bill at 3.5% discount gives a BEY of 3.6118%, which is the correct benchmark to compare against a bond paying a 3.5% coupon.

How is BEY calculated step by step?

First compute the discount factor: d * t / 360. For 3.5% and 180 days, that is 0.035 * 0.5 = 0.0175. Then the holding period return: 0.0175 / (1 - 0.0175) = 0.017812 (or 1.7812%). Finally, annualize: 0.017812 * (365 / 180) = 0.036118, so BEY = 3.6118%.

How does BEY differ from APY?

BEY uses simple interest annualization, while APY accounts for semiannual compounding. For a 180-day T-bill at 3.5% discount, BEY is 3.6118% but APY is 3.6444% — a 0.0326% difference from compounding. At higher rates the gap grows: a 182-day bill at 5.0% discount has BEY of 5.2009% vs APY of 5.2685%, a 0.0676% spread.

Why is BEY always higher than the stated discount yield?

Discount yield is based on face value, but you pay less than face value for the bond. Since your actual investment is smaller, the return on your investment is higher. For a 180-day T-bill at 3.5% discount, you pay $98.25 per $100 face, so your actual return (BEY 3.6118%) exceeds the discount yield. The BEY-vs-discount spread here is 0.0632%.

What does the effective price represent?

The effective price is what you pay per $100 of face value: Price = 100 * (1 - d * t / 360). At 3.5% discount for 180 days, you pay $98.25 and receive $100 at maturity — a $1.75 gain. At 5.0% discount for 182 days, the price drops to $97.4722, yielding a $2.5278 gain per $100 invested.

How does maturity length affect BEY?

Longer maturities increase the holding period return but the annualization factor (365/t) decreases. A 91-day T-bill at 5.0% discount yields BEY of 5.1343% with a 1.2801% holding period return. A 364-day T-bill at 4.5% discount yields BEY of 4.7800% with a 4.7669% holding period return — a lower annualized rate but far more total income per cycle.