Why are three different yields quoted for one bill?

Convention rather than substance. Discount yield is how the market talks, bond-equivalent yield is how it compares with other bonds, and effective annual yield is what it compounds to. The cash is identical.

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Treasury Bill Yield Calculator

The three yields a Treasury bill can be quoted at, and why they differ. The discount yield on a dealer screen is always the lowest of them, and it is not the return on your money.

Also called: t bill yield calculator, discount to yield.

Bond equivalent yield

6.11%

6.11% on a bond-equivalent basis. The discount yield of 5.93% that dealers quote is lower, because it divides the gain by face value rather than by what you actually paid.

Discount yield (dealer quote)

5.93%

Effective annual yield

6.25%

Gain at maturity

$15.00

Days held

How this is calculated

An estimate, not an offer or a guarantee. Projected returns assume the rate you entered holds for the whole term, which no market does.

Method and background

This is what the calculation gives for the numbers you entered. It is an estimate, not advice, and it knows nothing about your situation beyond those numbers. Rules for United States change on a published schedule; the effective date is shown on every rule-based tool.

How this is calculated

A bill pays no coupon; you buy below face and are repaid face. The dealer convention divides the gain by face value on a 360-day year, which understates the return twice over. The bond-equivalent yield divides by the price you actually paid on a 365-day year, so it compares with a coupon bond. The effective annual yield compounds that over a full year.

bond-equivalent yield divides by price on a 365-day year; discount yield divides by face on a 360-day year

F: Face value (currency)
P: Price paid (currency)
d: Days to maturity (days)

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a 91-day bill at 985

Face value: $1,000.00
Purchase price: $985.00
Days to maturity: 91

Bond equivalent yield6.11%

Worked by hand on both conventions; the dealer quote is the lower one

Open this example

buying at face yields nothing

Face value: $1,000.00
Purchase price: $1,000.00
Days to maturity: 91

Bond equivalent yield0%

degenerate case

Open this example

a full-year bill makes the two day-counts diverge most

Face value: $1,000.00
Purchase price: $950.00
Days to maturity: 365

Bond equivalent yield5.26%

boundary: 50/950 over exactly one year

Open this example

Method and limits

What it assumes

Held to maturity.

What it deliberately does not model

State and local tax exemption, which is a real part of the return, is not valued here.

Sources

TreasuryDirect. Treasury bills (primary government)

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

Why are three different yields quoted for one bill?: Convention rather than substance. Discount yield is how the market talks, bond-equivalent yield is how it compares with other bonds, and effective annual yield is what it compounds to. The cash is identical.