Treasury Bill Yield Calculator

Read the calculator result

A Treasury bill can be described by several yield percentages even when its purchase price and maturity payment are the same. This calculator starts with those cash amounts. Enter face value, purchase price, any separate transaction fee, and actual days remaining to maturity. It then distinguishes the holding-period return, the bank discount quotation, and two different annualization methods.

The tool doesn’t fetch an auction price, place an order, or predict the return available when a bill matures. Its example prices are illustrative. Use a confirmed price and the timing relevant to the transaction you’re evaluating, and compare yield labels before comparing the numbers.

TreasuryDirect’s bill overview explains that bills can be sold at a discount or at face value and pay face value at maturity. The difference between price and face value supplies the basic gross dollar return used here. This calculator’s return scenario assumes the stated maturity payment is received and doesn’t model selling early.

Treasury bill yield: enter face value, price, fees, and days consistently

Face value is the total amount assumed payable at maturity for the position you’re calculating. Purchase price is the total dollar price for that same position before the separately entered fee. Don’t mix a quote per $100 of face value with the dollar cost of a $10,000 position.

For example, a price of 99 per $100 of face value corresponds to $9,900 for $10,000 of face value. Enter $9,900 as the purchase price and $10,000 as face value. The worksheet doesn’t know whether a number copied from another screen is a price quotation or a total cash amount.

The fee field adds a separate transaction cost once. If the price you enter already includes that cost, don’t add it again. The calculator preserves both the gross discount before the fee and the net dollar return after the fee so a small charge can’t disappear inside a yield label.

Days to maturity means the actual entered holding interval for this comparison. It isn’t automatically the original term printed in a security description. The tool accepts a bounded interval from 1 to 366 days and doesn’t infer issue dates, settlement dates, holiday adjustments, or whether a bill with a particular original term is available.

How the calculator works

Gross discount = face value − purchase price. Total invested cash = purchase price + separate fee. Net dollar return = face value − total invested cash. These dollar amounts are the starting point for interpreting every percentage.

The gross holding-period yield divides the gross discount by purchase price. The net holding-period return divides the net dollar return by total invested cash. Each measures the return over the entered days, without pretending that the holding period is a whole year.

The calculator requires price at or below face value for this bill model. A par purchase with no fee produces zero return. A fee can exceed the discount and create a negative net return even though the purchase price itself is below face value. The tool retains that loss instead of clipping it to zero.

Why the bank discount yield is different

The bank discount yield uses face value as its denominator and a 360-day year: (face value − price) ÷ face value × 360 ÷ days. Multiply the decimal result by one hundred to express it as a percentage. It excludes the separately entered transaction fee.

TreasuryDirect’s pricing explanation presents bill price as face value multiplied by one minus the discount rate times days divided by 360. Rearranging that relationship gives the discount-yield formula used here. The 360-day convention is part of the quotation method; it doesn’t mean the tool has shortened your actual holding period.

A percentage based on face value differs from a return based on the smaller amount actually paid. The annualization basis can differ as well. Therefore, a discount yield and a purchase-price yield shouldn’t be treated as interchangeable numbers, even when both describe the same bill.

Understand the purchase-price annualizations

Simple annualization multiplies a holding-period return by the chosen comparison-year length divided by the entered days. You can select 365 or 366 days. The gross version uses purchase price and gross discount; the net version uses price plus the fee and the remaining dollar return.

The reinvestment-equivalent annual return instead compounds the same net holding-period growth factor over the year: [face value ÷ total invested cash] raised to [year days ÷ holding days], minus one. That’s a mathematical comparison requiring repeated equivalent growth. It doesn’t promise that another bill will offer the same return or that money can be reinvested immediately.

These labels also avoid a separate confusion. Treasury’s official formulas in Appendix B to 31 CFR Part 356 distinguish investment-rate calculations for bills of not more than one half-year from those longer than one half-year. The latter use a different coupon-equivalent relationship. This tool’s simple purchase-price annualization isn’t presented as the official investment rate for every maturity.

Treasury bill yield calculator example: $9,900 paid for $10,000 in 91 days

Assume a $10,000 face value, a $9,900 purchase price, no separate fee, and 91 days remaining. Select a 365-day comparison year. The gross discount and net dollar return both equal $100.

The position still earns $100 over 91 days under the stated assumptions. None of the larger annual percentages creates an additional payment during that period. The figures answer different measurement questions rather than describing different amounts of cash received.

Test price, fee, and term changes

Lower only the purchase price to $9,850. Gross and net return become $150. The holding-period return is approximately 1.5228%, bank discount yield 5.9341%, and simple annualization 6.1081%. The cash chart changes because the amount invested and the maturity gain actually changed.

Return to the $9,900 price and add a $25 fee. Total invested cash becomes $9,925, and net return falls to $75. The gross discount and its bank discount yield stay unchanged because that quotation excludes the separate fee. Net return measures decline. This is why a quoted yield alone can miss an investor-specific transaction cost.

If that fee were $150, total cash invested would be $10,050 against $10,000 received at maturity. The net dollar return would be −$50. A positive discount doesn’t prevent a negative result after all the entered cash costs.

Changing the day basis from 365 to 366 leaves price, proceeds, net dollars, and holding-period return unchanged. Simple annualized returns multiply by 366/365, while the bank discount yield still uses 360. The cash chart correctly remains identical; the separate return table changes.

Changing the holding interval answers a different question. Keep the $9,900 price, $10,000 face value, and zero fee, but enter 364 days instead of 91. The $100 gain and roughly 1.0101% holding-period return stay the same. Because the time interval is four times as long, the simple annualized return becomes one quarter of its earlier value, about 1.0129%. The bank discount yield also becomes one quarter of its earlier value, about 0.9890%.

This doesn’t predict the price of an actual longer bill. It holds price and proceeds fixed to isolate the time input. An actual comparison between two securities should use each security’s own confirmed price and remaining days, then retain the appropriate yield-convention labels.

Also keep principal and earnings separate. The $10,000 maturity proceeds include the $9,900 initially paid in the default example. Treating the entire maturity payment as income would count the returned principal as a new gain.

Use the cash chart and return table together

The chart displays the purchase price, separate fee, maturity proceeds, and net dollar return. Those bars are cash amounts, not a time series of market prices. A small gain may look short beside the entire principal, so the adjacent table supplies the exact values.

The second table identifies each return’s convention. Use it to check whether another source divides by face value or cash paid, includes a fee, uses a different year basis, or assumes compounding. A difference in labels can explain a difference in percentages without either calculation being an arithmetic error.

For a separate generic interest calculation using a contractual day basis, see the simple interest calculator. For annual yield comparisons involving different entered tax treatment, see the tax equivalent yield calculator. Neither tool automatically changes the bill’s entered cash amounts or establishes its tax treatment.

Treasury bill yield calculator questions

Does this calculate what I would receive if I sell early?

No. The modeled terminal payment is face value at maturity. An early sale needs an actual or assumed sale price, transaction costs, and its own holding interval. Replacing maturity proceeds with an unverified forecast would answer a different question.

Does choosing 366 days detect a leap-year convention automatically?

No. It’s an explicit comparison input. The calculator doesn’t inspect dates or determine which official convention applies to an auction. Verify the relevant documentation before using a result to reconcile a specific quoted investment rate.

Which displayed percentage is the money I earn?

The net dollar return is the money difference after the entered fee, while the net holding-period percentage relates that difference to invested cash. Annualized measures help with carefully labeled comparisons; they don’t guarantee a year of repeated earnings.