Why does the bank discount yield use 360 days instead of 365?

Bank discount yield is a convention dating to when calculations were done by hand — a 360-day year simplifies arithmetic. It does understate the true annualized return compared to a 365-day basis.

Which yield measure is most comparable to a corporate bond yield?

Bond Equivalent Yield (BEY) uses a 365-day year and is based on the purchase price rather than face value, making it the most comparable to coupon bond yields quoted on a semi-annual basis.

Can the purchase price of a T-bill exceed its face value?

No. T-bills are zero-coupon instruments sold at a discount to face value; you receive face value at maturity. The yield would be negative if the purchase price exceeded face value.

Treasury Bill Rate Calculator

Calculate the bank discount rate, money market yield, and bond equivalent yield for a Treasury bill given its face value, purchase price, and days to maturity.

By AbraCalc Editorial Team · Reviewed by AbraCalc Methodology Review · Last reviewed: 2026-06-25

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How to use this tool

Enter face value (par), purchase price and days to maturity in the fields above.
Results update instantly as you type — or click Calculate.
Read your bank discount yield (bdy) and the full breakdown beneath it.

⚠ This tool provides general estimates for education only and is not financial, tax or legal advice. Figures may not reflect your situation — verify with a qualified professional.

Formula

Bank Discount Yield: BDY = (D / F) × (360 / t)

Money Market Yield: MMY = (D / P) × (360 / t)

Bond Equivalent Yield: BEY = (D / P) × (365 / t)

where D = Face − Price, F = face value, P = purchase price, t = days to maturity.

How it works

Treasury bills are zero-coupon instruments sold at a discount to face value; the investor's return is the dollar discount (D = F − P) earned at maturity. The bank discount yield (BDY) is the traditional T-bill quotation convention, annualizing the discount relative to face value on a 360-day year.

The money market yield (MMY) is more economically accurate because it relates the gain to the amount actually invested (purchase price) rather than face value, still using a 360-day convention. The bond equivalent yield (BEY) converts to a 365-day year for comparison with coupon bonds. All three yields assume simple (not compounded) interest.

Worked example

91-Day T-Bill: Face $10,000, Price $9,800

Dollar discount D = $10,000 − $9,800 = $200.
Bank Discount Yield = ($200 / $10,000) × (360 / 91) = 0.02 × 3.9560 = 7.912%.
Money Market Yield = ($200 / $9,800) × (360 / 91) = 0.020408 × 3.9560 = 8.074%.
Bond Equivalent Yield = ($200 / $9,800) × (365 / 91) = 0.020408 × 4.0110 = 8.186%.

BDY = 7.9121%, MMY = 8.0736%, BEY = 8.1857%.

Common mistakes to avoid

Using calendar days (365) in the bank discount yield formula when it requires a 360-day year, producing an understated BDY.
Confusing the purchase price with the face value when calculating the discount — the discount is face minus price, not the other way around.
Comparing T-bill BDY directly with bond yields without converting to bond equivalent yield (BEY) first, since BDY understates the effective return.

Key terms

Bank Discount Yield (BDY): The traditional T-bill yield quotation, computed as the dollar discount divided by face value, annualized on a 360-day basis.
Money Market Yield (MMY): T-bill yield calculated relative to the purchase price (invested amount), annualized on a 360-day basis; directly comparable to money market instruments.
Bond Equivalent Yield (BEY): The T-bill yield expressed on a 365-day basis to allow comparison with coupon-paying bonds.
Dollar Discount (D): The difference between face value and purchase price of a Treasury bill; represents the investor's total return at maturity.
Face Value (Par): The amount paid to the T-bill holder at maturity, typically $1,000 or $10,000.

Frequently asked questions

Why does the bank discount yield use 360 days instead of 365?: Bank discount yield is a convention dating to when calculations were done by hand — a 360-day year simplifies arithmetic. It does understate the true annualized return compared to a 365-day basis.
Which yield measure is most comparable to a corporate bond yield?: Bond Equivalent Yield (BEY) uses a 365-day year and is based on the purchase price rather than face value, making it the most comparable to coupon bond yields quoted on a semi-annual basis.
Can the purchase price of a T-bill exceed its face value?: No. T-bills are zero-coupon instruments sold at a discount to face value; you receive face value at maturity. The yield would be negative if the purchase price exceeded face value.