The short answer
For the TreasuryDirect bill formula, price = face value × [1 − discount rate × days ÷ 360]. The discount rate uses face value as its base; your purchase outlay is a different number.
First identify the security and the field
TreasuryDirect describes bills as securities maturing in one year or less, sold at face value or at a discount. At maturity, Treasury pays the face value; the difference between that value and the discounted purchase price is interest. This is different from reading the coupon on a note or bond.[5]
Before calculating, make a four-field record: security type, face amount, discount rate and the number of days in the pricing period. Keep the source’s exact field label. A number called a yield, investment rate or coupon should not be inserted into a discount-rate formula simply because it is also expressed as a percentage.
Use the 360-day denominator in the stated formula
The official bill formula is price = face value × [1 − (discount rate × time) ÷ 360]. TreasuryDirect illustrates time with a number of days. Convert the rate from a percentage to a decimal first: a hypothetical 4% becomes 0.04, not 4.[5]
The 360 in this formula is a calculation convention, not a claim that the calendar year has 360 days. Do not silently substitute 365 and still label the result as the official discount-price calculation. Do not substitute the number of weeks for the number of days either.
A complete hypothetical 91-day example
Assume a face amount of $1,000, 91 days and a 4% discount rate. These are invented teaching inputs, not a September 2026 quote. The price is 1,000 × [1 − (0.04 × 91 ÷ 360)] = $989.888888…, or $989.89 when rounded to cents for illustration. The unrounded discount is $10.111111….
Using the unrounded values, the difference divided by face value is about 1.0111%. The same difference divided by the purchase price is about 1.0214%. The second number describes the gross holding-period return on this hypothetical outlay if held to maturity; neither number is an annual percentage yield. Fees and taxes are not modeled.
Read a price per $100 correctly
TreasuryDirect says the auction-result price displayed in the relevant account view is for each $100 of the bid. That is a unit label, not an instruction that the entire purchase costs only the displayed number.[2]
In the hypothetical example, the price per $100 face amount is 98.988888…. Multiplying by 1,000 ÷ 100 gives the same $989.888888… outlay. Keep extra precision until the final arithmetic, but use the actual award statement—not this illustration—to establish the amount due and any official rounding.
Separate the auction date from the cash date
The official auction description lists auction, issue and maturity dates separately and says the money is taken from the designated account when the securities are issued. The auction date and issue date can differ.[2]
For a comparison worksheet, retain the actual issue and maturity dates and the source’s pricing period. Do not start the day count from the date you happened to read an auction announcement. Record the date of the result as well: an educational page’s review date is not the date of an available rate.
What this calculation does not settle
This worksheet explains one quoted-rate convention. It does not rank bills against a savings account, predict a reinvestment rate or calculate your after-tax outcome. If comparing alternatives, request a clearly specified annualization method and equal holding periods rather than comparing two bare percentages.
An early-sale quote is outside this worked example. The maturity face amount should not be presented as a guaranteed price available before maturity. Save the actual security identifier, official result, cash amount, maturity date and any intermediary fees before using the arithmetic for a real decision.
Sources & scope
Links support definitions and methodology. Worked examples are hypothetical, not quotes; the review date is not the observation date of a market value.
- TreasuryDirect — Understanding Pricing and Interest Rates ↗
Source date: Not stated in the retrieved body · Verified: 2026-09-20
- TreasuryDirect — How Auctions Work ↗
Source date: Not stated in the retrieved body · Verified: 2026-09-20