Treasury Bills: Discount Rate vs. Investment Yield Explained

Treasury bills quote two distinct yields because of a century-old institutional accounting convention: the discount rate measures your price discount against face value across an artificial 360-day year, while the investment yield (or coupon-equivalent yield) measures your true annualized return on the cash actually invested over a full 365-day calendar year. Because the purchase price is always lower than the face value, the investment yield is always higher than the quoted discount rate—often by 10 to 30 basis points.

Contents

• Why Treasury Bills Quote Two Different Rates
• The Core Formulas: Price, Discount, and Investment Yield
• Step-by-Step Worked Example on a $10,000 Bill
• Comparing Yields Across T-Bill Maturities
• Compounding Frequency and the State Tax Shield
• Common Mistakes Cash Investors Make
• Related Concepts and Next Steps
• Sources & Further Reading

Why Treasury Bills Quote Two Different Rates

When you participate in a U.S. Treasury auction or view secondary market quotes on TreasuryDirect Treasury Bills, every auction result displays two headline percentage figures: the High Rate (the clearing discount rate) and the Investment Rate. For novice investors, this dual quotation often leads to confusion. A 26-week bill might clear at a 4.80% discount rate, but display an investment rate of 4.99%.

This gap is not an added fee, commission, or dealer spread. Rather, it reflects two fundamentally different mathematical perspectives on debt pricing:

• The Bank Discount Convention: Developed for money market dealers in the early 20th century, the discount rate treats the bill as a commercial instrument. It calculates the annualized discount relative to the face value (par) that the government repays at maturity, standardizing all calculations on a simplified 360-day commercial banking year (twelve 30-day months).
• The Investment Yield Convention: Standard bond market analytics—and retail financial planning—evaluate return on capital. The investment yield (also known as the coupon-equivalent yield or bond-equivalent yield) calculates the return on the actual cash out of pocket spent to acquire the security, scaled to the actual 365-day calendar year.

As documented by primary debt issuance guidelines, bills are sold at a discount or at par (face value). When the bill matures, you are paid its face value. You can hold a bill until it matures or sell it before it matures. Because the amount you invest is smaller than the face value you collect, your economic return per dollar at risk is necessarily greater than the discount percentage indicates.

The Core Formulas: Price, Discount, and Investment Yield

To evaluate Treasury bills accurately, an investor needs to understand two equations: how the Treasury auction discount rate determines the purchase price, and how that purchase price translates into the annualized investment rate.

1. Calculating Purchase Price from the Discount Rate

The purchase price per $100 of face value is derived by subtracting the annualized discount from par using a 360-day year:

Price = Face Value × [1 - (Discount Rate × Days to Maturity / 360)]

In this formula, Face Value is typically normalized to $100 (or the full principal, such as $10,000), Discount Rate is expressed as a decimal (e.g., 0.048 for 4.80%), and Days to Maturity represents the actual number of calendar days between settlement and redemption.

2. Calculating the Investment Rate (Coupon-Equivalent Yield)

Once the purchase price is known, the true annualized yield on the capital committed is calculated using the actual 365-day calendar year:

Investment Yield = [(Face Value - Price) / Price] × (365 / Days to Maturity)

Notice the two mathematical forces that make the investment yield systematically higher than the discount rate:

1. Smaller Denominator: The discount rate divides the dollar gain by Face Value, whereas the investment yield divides that exact same dollar gain by Price. Because Price < Face Value, the ratio is inherently larger.
2. Larger Calendar Multiplier: The discount formula annualizes using 360 / Days, while the investment formula annualizes using 365 / Days. Multiplying by 365 instead of 360 increases the calculated rate by a factor of 1.0139 (roughly 1.4%).

Step-by-Step Worked Example on a $10,000 Bill

Consider an illustrative example of an investor purchasing a 26-week (182-day) Treasury bill with a face value of $10,000 at a hypothetical auction discount rate of 4.80%.

Step 1: Determine the Dollar Discount and Cash Purchase Price

Using the price formula:

Discount Amount = $10,000 × 0.0480 × (182 / 360) = $242.67
Purchase Price = $10,000 - $242.67 = $9,757.33

The investor wires exactly $9,757.33 on settlement day. No additional brokerage commissions or transaction fees apply on direct TreasuryDirect purchases or major non-commission brokerage platforms.

Step 2: Calculate the Unannualized Holding Period Return

Over the 182-day holding period, the investor earns $242.67 on an investment of $9,757.33:

Holding Period Return = $242.67 / $9,757.33 = 0.0248705 (2.4871%)

Step 3: Annualize to Derive the Investment Rate

To convert this 182-day return into an annualized coupon-equivalent yield, multiply by the 365-day annualization factor:

Investment Yield = 2.48705% × (365 / 182) = 2.48705% × 2.0054945 = 4.9878% ≈ 4.99%

The resulting investment rate of 4.99% is roughly 19 basis points higher than the 4.80% discount rate. If an investor mistakenly evaluated this bill using its 4.80% discount rate against a bank certificate of deposit offering 4.90% APY, they would have incorrectly concluded that the CD offered the superior yield.

Comparing Yields Across T-Bill Maturities

The difference between the discount rate and the investment rate expands as the maturity lengthens. For a 4-week bill, the price paid is very close to par, so the denominator effect is small. For a 52-week bill, the dollar discount is substantial, amplifying the divergence.

The table below summarizes the exact mathematical relationship across standard Treasury bill auction tenors, assuming a constant hypothetical 4.80% discount rate on a $10,000 face value commitment:

Maturity Term	Days	Purchase Price	Dollar Discount	Discount Rate	Investment Yield	Yield Spread
4-Week	28	$9,962.67	$37.33	4.80%	4.88%	+8 bps
8-Week	56	$9,925.33	$74.67	4.80%	4.91%	+11 bps
13-Week	91	$9,878.67	$121.33	4.80%	4.93%	+13 bps
26-Week	182	$9,757.33	$242.67	4.80%	4.99%	+19 bps
52-Week	364	$9,514.67	$485.33	4.80%	5.12%	+32 bps

Compounding Frequency and the State Tax Shield

Understanding the difference between discount and investment rates is essential, but two other structural features directly impact the net money an investor keeps: compounding frequency and tax treatment.

Annual Percentage Yield (APY) and Reinvestment Compounding

The investment yield published by the Treasury is a simple annual percentage rate (APR) designed to match the semiannual coupon payment convention of longer-term Treasury notes. However, because Treasury bills mature in one year or less, an investor who continually reinvests maturing principal and interest realizes compounding gains.

For example, if an investor purchases a 26-week bill yielding an unannualized 2.4871% per half-year, and rolls the full proceeds into a second 26-week bill at the same yield, the effective annual yield (EAY) becomes:

Effective Annual Yield = (1 + 0.0248705)² - 1 = 1.05036 - 1 = 5.036% ≈ 5.04%

This compounding effect pushes the realized return above even the quoted 4.99% investment rate, demonstrating why short-term bill ladders can outperform static cash instruments.

The State and Local Tax Exemption

Unlike commercial bank CDs, money market deposit accounts, or corporate commercial paper, U.S. government obligations carry a statutory tax exemption from sub-federal taxation. As codified in IRS Publication 550, interest income from Treasury bills, notes, and bonds is subject to federal income tax but is exempt from all state and local income taxes.

For an investor residing in a state with an 8% state income tax bracket, a Treasury bill offering an illustrative 5.00% investment yield delivers the same after-tax cash as a taxable bank CD yielding 5.43%:

Equivalent Taxable Yield = Treasury Yield / (1 - State Tax Rate) = 5.00% / (1 - 0.08) = 5.43%

Investors interested in evaluating state tax impacts across municipal and federal obligations can explore our comprehensive breakdown on tax-equivalent yield.

Common Mistakes Cash Investors Make

• Comparing Discount Rate Directly to CD APY: Banks market retail certificates of deposit using Annual Percentage Yield (APY), which reflects daily or monthly compounding over 365 days. Comparing a T-bill’s 360-day discount rate to a bank’s 365-day APY severely underestimates the Treasury’s relative return. Always compare a bank CD’s APY to the T-bill’s investment rate or its effective annual compound yield.
• Ignoring Secondary Market Accrued Value: If you sell a Treasury bill before maturity in the secondary market, you do not receive a coupon. Instead, the market price of the bill rises toward par as maturity approaches. Your realized gain depends on prevailing interest rates at the time of sale, which could result in a modest capital loss if interest rates have surged since purchase.
• Misunderstanding Maturity Schedules: As outlined by federal guidelines, Treasury bills generally have maturity terms of 4 weeks, 8 weeks, 13 weeks, 17 weeks, 26 weeks, or 52 weeks. Cash management bills (CMBs) also exist for variable short tenors, but CMBs are typically auctioned for institutional liquidity needs rather than regular retail schedules.

Related Concepts and Next Steps

Treasury bills are the foundation of short-term risk-free rates and monetary plumbing. To broaden your understanding of fixed-income markets, explore these related guides:

• Treasury Securities 101: How bills, notes, and bonds fit together across the yield curve.
• Zero-Coupon Bonds and STRIPS: How longer-term zero-coupon Treasuries price and how phantom tax rules apply.
• Tax-Equivalent Yield Explained: How to mathematically compare municipal bonds, Treasuries, and taxable debt.
• ECMSource Learning Hub: Our curated directory for fundamental equity and debt capital market concepts.

Sources & Further Reading

• TreasuryDirect: Treasury Bills In Depth — Official issuance details, terms, bidding mechanics, and redemption rules.
• IRS Publication 550 (Investment Income and Expenses) — Chapter 1: U.S. Treasury bills, notes, and bonds taxation and state tax exemptions.
• ECMSource: Tax-Equivalent Yield: How to Compare Munis and Treasuries — Mathematical formulas for after-tax bond comparisons.
• ECMSource: Educational Hub and Research Index — Guide to fixed income, capital markets, and corporate valuation.

Disclosure: This article is for informational purposes only and is not investment advice.