Calcady™

Treasury Bill Yield Calculator

Calculate the Bond Equivalent Yield (BEY) of a U.S. Treasury Bill, and compare it against the Bank Discount Yield (BDY) money market convention.
Wealth & Investment
Standard: 31 CFR Part 356 Appendix B / Treasury Bill Yield Formulas

Secondary Market Quotes

$
$

Time Horizon

Days
The number of calendar days remaining until maturity redemption.
Calculated result for Bond Equivalent Yield (BEY):

Bond Equivalent Yield (BEY)

4.138%
Annualized investment yield on invested principal.
Calculated result for Bank Discount Yield (BDY):

Bank Discount Yield (BDY)

4.000%
Quoted discount basis under money market conventions.
Total Discount Gain
$200.00
Holding Period
180 days

Yield Convention Spread

Yield Spread (BEY - BDY):+0.138%

Methodology Comparison: BDY divides the $$200.00 discount by the $$10,000.00 face value on a 360-day basis (4.000%). BEY measures the return against the actual $$9,800.00 cash invested over a 365-day year, resulting in an annualized return of 4.138%.

Interactive Treasury Bill Yield Walkthrough

Money market Bank Discount Yield (360-day) vs Bond Equivalent Yield (365-day) derivation

31 CFR Part 356 Appendix B / Money Market Conventions
Design Scenario

Analyzing U.S. Treasury bill with Face Value = $10,000.00, Purchase Price = $9,800.00, and 180 days remaining to maturity.

Mathematical Solution
1Calculate Dollar Discount From Par

Capital gain realized at redemption upon maturity.

D = $10,000.00 - $9,800.00 = $200.00
2Calculate Bank Discount Yield (BDY / Quoted Rate)

Standard institutional quote convention based on face value and commercial 360-day year.

\text{BDY} = \left(\frac{$200.00}{$10,000.00}\right) \times \left(\frac{360}{180}\right) \times 100 = 4.000\%
4.000% BDY
3Compute Bond Equivalent Yield (BEY / Investment Yield)

True annualized economic return on actual cash capital invested over an authentic 365-day calendar year (t <= 182 days).

\text{BEY} = \left(\frac{$200.00}{$9,800.00}\right) \times \left(\frac{365}{180}\right) \times 100 = 4.138\%
4.138% BEY
4Analyze Convention Basis Spread

BEY consistently exceeds BDY because P < F and 365 > 360, properly comparing short paper to coupon-bearing notes.

\Delta Y = 4.138\% - 4.000\% = +0.138\%
+0.138% Spread
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What is T-Bill Yield Mechanics: BEY vs BDY?

Unlike fixed-coupon notes and bonds that distribute periodic coupon checks, U.S. Treasury Bills (T-Bills) are discount instruments issued without coupons. Investors acquire them below face value, and the U.S. Treasury redeems them at par upon maturity. Money market quoting conventions distinguish between discount rates and true investment yields.

Mathematical Foundation

BDY=DF×360tBDY = \frac{D}{F} \times \frac{360}{t}
BDYBDY= Bank Discount Yield. Standard market quotation method for discount paper.
DD= Discount Amount (Face Value minus Purchase Price).
FF= Face Value (Par redemption amount at maturity).
360360= Traditional commercial paper calendar convention (12 months of 30 days).
BEY≤182=DP×365tBEY_{\le 182} = \frac{D}{P} \times \frac{365}{t}
BEY≤182BEY_{\le 182}= Bond Equivalent Yield for maturities of 182 days or fewer (simple interest annualization).
PP= Purchase Price (Actual capital invested).
365365= Standard calendar year day count (366 in leap years).
BEY>182=−2(t/365)+2(t/365)2−(2(t/365)−1)(1−F/P)2(t/365)−1BEY_{> 182} = \frac{-2(t/365) + 2\sqrt{(t/365)^2 - (2(t/365)-1)(1 - F/P)}}{2(t/365) - 1}
BEY>182BEY_{> 182}= Bond Equivalent Yield per 31 CFR Part 356 Appendix B for bills over 182 days.
t/365t / 365= Maturity ratio of days to full calendar year.
F/PF / P= Ratio of face value redemption to purchase price, incorporating semiannual compounding.

Laws & Principles

  • Denominator Convention Difference: The Bank Discount Yield (BDY) divides discount dollars by the face value of the bill. In contrast, Bond Equivalent Yield (BEY) evaluates return against the actual discounted purchase price, aligning with standard internal rate of return conventions.
  • Day-Count Convention: BDY annualizes using a 360-day money market baseline, while BEY annualizes using a full 365-day calendar year, making BEY higher than BDY under positive discount conditions.
  • 31 CFR Part 356 Appendix B Compounding Rule: For Treasury bills maturing in 182 days or fewer, BEY uses simple annualization. For bills maturing in more than 182 days (such as 52-week bills), Treasury regulations mandate a semiannual compounding equivalent formula so yields are directly comparable to semiannual coupon-paying Treasury notes and bonds.
  • Investment Yield Comparison: BEY allows direct comparison between non-interest-bearing discount bills and traditional coupon-bearing Treasury notes or corporate bonds.

Step-by-Step Example Walkthrough

" A Treasury bill with a $10,000 face value is purchased for $9,800 maturing in 180 days. "

  1. Calculate Discount (D): $10,000 − $9,800 = $200.
  2. Calculate BDY: ($200 ÷ $10,000) × (360 ÷ 180) = 4.000%.
  3. Calculate BEY: ($200 ÷ $9,800) × (365 ÷ 180) = 4.137%.
Final Result: While quoted on a 4.000% discount basis (BDY), the annualized investment yield on the $9,800 outlay is 4.137% (BEY).

Quick Answer: What is the true yield of a T-Bill?

The annualized return on invested capital for a Treasury Bill is the Bond Equivalent Yield (BEY), which evaluates return on the cash outlay using a 365-day year. Institutional markets quote discount paper on a Bank Discount Yield (BDY) basis (measured against par value using a 360-day count). Use the calculator to compare BDY quotes against effective BEY yields.

Yield Methodology Comparison

BDY (Discount Quote)

BDY = (D ÷ F) × (360 ÷ t)

BEY (Investment Yield)

BEY = (D ÷ P) × (365 ÷ t)

Bank Discount Yield Characteristics

  • Uses face redemption value (F) as the denominator.
  • Annualizes using a 360-day banker year.
  • Standard quotation method in financial press and dealer screens.

Bond Equivalent Yield Characteristics

  • Uses actual purchase outlay (P) as the denominator.
  • Annualizes using a 365-day calendar year.
  • Enables apples-to-apples comparison with coupon-paying fixed income.

Comparing Short vs Long Maturities

Scenario A: 4-Week T-Bill

$10,000 face value bought for $9,960 (28 days to maturity).

  1. Total Discount: $40
  2. Quoted Discount (BDY): ($40 ÷ $10,000) × (360 ÷ 28) = 5.143%
  3. Investment Yield (BEY): ($40 ÷ $9,960) × (365 ÷ 28) = 5.236%

→ The investment yield reflects a +0.093% spread above the quoted discount rate.

Scenario B: 52-Week T-Bill

$10,000 face value bought for $9,500 (364 days to maturity).

  1. Total Discount: $500
  2. Quoted Discount (BDY): ($500 ÷ $10,000) × (360 ÷ 364) = 4.945%
  3. Investment Yield (BEY): ($500 ÷ $9,500) × (365 ÷ 364) = 5.278%

→ For longer maturities with deeper discounts, the spread between BEY and BDY expands.

Treasury Bill Specifications

Duration Auction Frequency Primary Use Case
4-WeekWeekly (Thursdays)Short-term liquidity management
8-WeekWeekly (Thursdays)Intermediate cash flow alignment
13-Week (3M)Weekly (Mondays)Standard short-term benchmark rate reference
26-Week (6M)Weekly (Mondays)Six-month reserve allocation
52-Week (1Y)Every 4 WeeksOne-year sovereign duration positioning

Treasury Cash Management Guidelines

Do This

  • ✓Factor in State Tax Exemption. Treasury bill interest is exempt from state and local income taxes under 31 U.S.C. § 3124, increasing after-tax yields relative to fully taxable commercial bank deposits.
  • ✓Evaluate Laddering Strategies. Staggering maturities across multiple settlement dates provides periodic liquidity while maintaining blended short-term yields.

Avoid This

  • ✗Don't confuse discount rate with coupon yield. Quoted discount yields understate effective annualized yield on invested capital because they reference par redemption rather than purchase cost.
  • ✗Don't ignore secondary market price fluctuations. While default risk on U.S. sovereign debt is minimal, selling before maturity exposes holdings to market interest rate movements.

Frequently Asked Questions

Why are Treasury Bills issued at a discount rather than paying coupons?

Short-term money market instruments are structured as discount paper to simplify administrative processing. Rather than distributing interim coupon payments over short durations (4 to 52 weeks), the investor's return is realized as the difference between the discounted auction price and the par value received at maturity.

Can Treasury Bills be sold prior to maturity?

Yes. Treasury bills held within standard brokerage custody can be sold on the secondary market prior to maturity at prevailing market rates. If interest rates have risen since purchase, secondary market value may be lower than amortized cost.

How do Treasury Bills compare in risk to FDIC-insured deposits?

Both instruments carry sovereign backing: bank accounts are insured up to statutory FDIC limits ($250,000 per depositor per institution), while Treasury bills represent direct debt obligations backed by the full faith and credit of the U.S. government without dollar cap limits.

How is Treasury Bill income taxed?

The discount realized at maturity is treated as ordinary interest income subject to federal income taxation, reported on Form 1099-INT. However, it is explicitly exempt from state and local income taxes.

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Calculation Provenance & Validation Record

Method

Treasury Bill Bank Discount Yield (BDY) vs Bond Equivalent Yield (BEY)

Formula
BDY=F−PF×360t×100,BEY=F−PP×365t×100\text{BDY} = \frac{F - P}{F} \times \frac{360}{t} \times 100, \quad \text{BEY} = \frac{F - P}{P} \times \frac{365}{t} \times 100
Assumptions
  • Bank Discount Yield (BDY) uses face value as denominator and annualizes via a 360-day year convention.
  • Bond Equivalent Yield (BEY) uses actual purchase price as denominator and annualizes via a 365-day year convention.
  • Calculations reflect nominal short-term money market conventions for Treasury bills held to maturity.
  • Excludes transaction fees, bid-ask spreads, and state or federal marginal income tax liabilities.
References
  • US Treasury Bill Money Market Yield Calculation Conventions (31 CFR Part 356) (31 CFR § 356.20 & Federal Reserve Bank Money Market Yield Standards) — 31 CFR § 356 Appendix B (Formulas for Treasury Bills: Discount Rate & Investment Rate)
Last substantive review:
Automated test status: 4 golden test vectors passing (TB-01, TB-02, TB-03, TB-04)
Method & assumptions

Calculation Methodology

Financial modeling and scenario projections based on standard time-value-of-money and compounding formulas.

Governing Standard Federal Reserve / US Treasury Money Market Conventions (31 CFR Part 356)

Standard:Treasury Direct Discount Yield (360-day)

Key Assumptions & Constraints

  • Bank Discount Yield (BDY) uses face value as denominator and annualizes via a 360-day year convention.
  • Bond Equivalent Yield (BEY) uses actual purchase price as denominator and annualizes via a 365-day year convention.
  • Calculations reflect nominal short-term money market conventions for Treasury bills held to maturity.
  • Excludes transaction fees, bid-ask spreads, and state or federal marginal income tax liabilities.
Financial Disclaimer: Calculations are educational estimates based on constant mathematical models. They do not account for market fluctuations, taxes, fees, or individual underwriting approval. Consult a certified financial professional.