Enter T-Bill Details

$
T-bills are sold in $100 increments
$
Total dollars paid (e.g., $9,875 on $10,000 face)
days
Standard tenors: 28, 56, 91, 119, 182, or 364 days
T-Bill Yield Formulas
BDY = (F - P) / F x (360 / d)
Bank Discount Yield (dealer quote)
BEY = (F - P) / P x (365 / d)
Bond Equivalent Yield (for d ≤ 182)
Ryan O'Connell, CFA
Calculator by Ryan O'Connell, CFA

Yield Results

Dollar Discount $125.00
Bank Discount Yield 4.945% Dealer quote convention
Bond Equivalent Yield 5.077%
Money Market Yield 5.008% CD-equivalent yield
Holding Period Return 1.266% Actual return over period
Effective Annual Yield 5.175% Compound annual return
For discount T-bills: BDY < MMY < BEY (when comparing the same bill)

Formula Breakdown

Model Assumptions
  • Bank discount yield uses Actual/360 day count (money market convention)
  • BEY uses simple formula for bills ≤182 days, Treasury quadratic formula for >182 days
  • EAY assumes reinvestment at same rate for full year (hypothetical)
  • 365-day year approximation (official Treasury uses 365 or 366)
  • No transaction costs, taxes, or bid-ask spreads

For educational purposes. Not financial advice.

Understanding T-Bill Yields

Why Are There Multiple Yield Measures?

Treasury bills are discount instruments: you pay less than face value today and receive face value at maturity. The difference is your return. However, there are several ways to express this return as an annualized yield, each with a different purpose:

Bank Discount Yield

Dealer quoting convention
Uses face value and 360-day year. Understates true return but is the standard way T-bills are quoted in the market.

Bond Equivalent Yield

Coupon bond comparison
Uses purchase price and 365-day year. Makes T-bill yields comparable to semiannual coupon bonds.

Standard T-Bill Maturities

The U.S. Treasury issues T-bills at regular auctions with the following standard maturities:

  • 4-week (28 days) - Weekly auction
  • 8-week (56 days) - Weekly auction
  • 13-week (91 days) - Weekly auction
  • 17-week (119 days) - Weekly auction
  • 26-week (182 days) - Weekly auction
  • 52-week (364 days) - Monthly auction

Cash management bills (CMBs) may be issued with non-standard maturities as needed.

Treasury's Official BEY Formula

For bills with more than 182 days to maturity, the Treasury uses a more complex formula that accounts for semiannual compounding. This calculator automatically switches to the official Treasury quadratic formula (per 31 CFR 356 Appendix B) when days exceed 182.

Important: Bank discount yield is a quoting convention, not a true measure of return. Always use BEY or EAY when comparing T-bill returns to other investments.

Frequently Asked Questions

Bank discount yield is the standard quoting convention for Treasury bills. It calculates annualized yield using face value as the denominator and a 360-day year: BDY = (Face - Price) / Face x (360 / Days). Because it uses face value rather than actual investment, it understates the true return compared to other yield measures.

Bond equivalent yield restates the T-bill return using the actual purchase price as the denominator and a 365-day year for bills of 182 days or less. For bills over 182 days, Treasury uses a more complex semiannual coupon-equivalent formula. BEY makes T-bill yields comparable to coupon bonds quoted on a semiannual basis.

For discount T-bills (priced below face value), BEY is higher for two reasons: (1) it uses the lower purchase price in the denominator instead of face value, producing a larger ratio, and (2) for short-term bills, it uses 365 days instead of 360, which slightly increases the annualization factor.

Money market yield (also called CD-equivalent yield) uses the purchase price as the denominator like BEY, but retains the 360-day year convention used in money markets: MMY = (Face - Price) / Price x (360 / Days). For discount bills, it falls between bank discount yield and BEY.

T-bills are quoted using bank discount yield, which understates true return. Convert to bond equivalent yield (BEY) for comparison with other bonds, or to effective annual yield (EAY) for the true compound annual return. Holding period return shows your actual dollar return over the holding period without annualization.

Effective annual yield (EAY) is the compound annual return, calculated as EAY = (1 + HPR)^(365/Days) - 1. It shows what your return would be if you could reinvest at the same rate for a full year. EAY is hypothetical because the reinvestment assumption is built into the calculation.
Disclaimer

This calculator is for educational purposes only. Results are based on simplified assumptions and may not match exact Treasury yields due to day count conventions (365 vs 366), settlement timing, and other factors. For official yields, refer to TreasuryDirect.gov. This tool should not be used for trading decisions.

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