TBILLEQ Function (Gnumeric)

• Introduced: Recorded as implemented in the grouped Gnumeric 0.33, 0.34 and 0.35 release notes. Those notes do not isolate which of the three releases first contained it, so the precise first version and release date remain unestablished.
• Documented support: Registered in Gnumeric 1.12.62, in the Financial Functions plugin. No retirement is established.
• Last functioning version: Unverified for this guide; source presence does not certify an application execution.
• Scope and dates: English formulas are shown. Official source snapshots were retained from the October 13–14, 2026 audit. This full guide and its reference calculations were checked on October 15, 2026; no newer source retrieval or native run is implied.

The inspected Gnumeric callback returns 365*discount/(360-discount*days). It describes this as a bond-equivalent yield for a treasury bill. The implementation uses this single expression across its accepted interval, including intervals above half a year; this guide does not substitute an alternative market formula for the actual Gnumeric code.

The function-specific help and complete callback provide the product-specific contract.

=TBILLEQ(settlement,maturity,discount)

• settlement: Valid starting date.
• maturity: Valid ending date, no more than 365 days later.
• discount: Nonnegative annual discount rate, entered as a fraction or percentage. All three arguments are required; the function has no basis parameter.

The registration was checked alongside the callback; use the exact function name and argument order rather than assuming cross-application equivalence.

Enter =DATE(2026,1,1) in B2, =DATE(2026,6,30) in B3 and discount 5% in B4. The date difference is 180. In B6 enter =TBILLEQ(B2,B3,B4). The reference value is approximately 0.051994301994, or 5.199430199430%. The denominator is 360-0.05*180=351; the numerator is 365*0.05=18.25. Dividing these provides an independent check.

The result is an annualized rate, not a per-100 price. The matching TBILLPRICE reference is 97.5, so a price and an annualized return should not be compared directly just because they use the same dates and discount input.

All outputs below are source-derived independent reference results. Decimal outputs are rounded to twelve places where needed. Use DATE expressions as written for date-based examples rather than substituting ambiguous date text.

For an accepted positive interval and a strictly positive implied price, TBILLEQ equals the corresponding TBILLYIELD multiplied by 365/360. This cross-check does not extend to zero or negative implied prices, because TBILLYIELD rejects them even when TBILLEQ returns a numeric result. For the sample, TBILLYIELD is approximately 5.128205128205%; scaling it gives 5.199430199430%. This identity follows by substituting 100*(1-discount*days/360) into the price-based yield formula. It helps isolate whether a mismatch is caused by a 360-day versus 365-day annualization convention.

At identical settlement and maturity dates, this callback still returns 365*discount/360, approximately 5.069444444444% for a 5% discount. That is an accepted algebraic boundary, not a meaningful positive holding-period yield. TBILLYIELD would reject the same zero-day interval.

The callback returns #NUM! for reversed dates, a negative discount, or an interval over 365 days. It separately returns #DIV/0! when 360-discount*days equals zero. The guard tests equality, not positivity. With a 180-day interval, discount 2 produces a zero denominator and an error; discount 3 produces a negative result. Validate that the implied price and denominator are positive for ordinary bill analysis.

The date arguments are passed through the shared integer-serial conversion helper. Use valid whole dates from DATE and check the difference; localized text, invalid dates and time portions have not been executed here. The guide describes Gnumeric’s pinned algorithm, not a guarantee that its yield convention meets every quotation, regulatory or trading requirement. Independently choose the required financial convention before using this result operationally.

The fixtures use explicit strings or valid numeric arguments and dates. Native blank/text coercions, localized formula entry and display formatting remain unverified; keep missing inputs distinct from intentional zero.

• Pinned worksheet implementation
• Pinned function help
• Additional helper source

The calculations are an independent reference model, not execution of the full Gnumeric engine, headless application or graphical editor. No exact installed-release behavior, GUI entry, locale handling, import parity or extreme-value outcome is certified beyond the stated source scope. Reproduce a small fixture in the target build before relying on an operational workbook.

TBILLPRICE, TBILLYIELD.