TBILLEQ in LibreOffice Calc: Treasury Bill Yield and Date Examples

• Introduced: First release not established; documented by LibreOffice 3.3.
• Supported in: 26.8 Help and 26.8.1.1 registration. No retirement is established.
• Scope: Desktop Calc with three date/discount arguments. The examples use English names and semicolons.
• Checked: October 14, 2026. Eight ordinary formulas recalculated in LibreOfficeDev 26.8.0.0.alpha0 through headless XLSX import. Complete wrapper guards, stable releases and GUI behavior remain untested.

TBILLEQ converts a treasury bill’s quoted discount into a bond-equivalent annual yield. The quoted discount and the investment return use different denominators: the discount is measured against the amount repaid at maturity, while the investor’s return is measured against the lower purchase price.

The result is a decimal rate. A result of 0.094151493566 means approximately 9.415149%, not 0.094151%. Changing the cell to Percentage changes its display, not the underlying calculation. The function has no face-value argument because scaling both the purchase price and repayment by the same amount leaves their return ratio unchanged. Function-specific Help.

TBILLEQ(Settlement; Maturity; Discount)

All three arguments are required:

• Settlement: the purchase date, entered as a real date value or constructed with DATE.
• Maturity: the repayment date. The checked Help describes maturity within the same year; every example here uses later dates in the same calendar year.
• Discount: the annual quoted discount as a decimal, such as 0.05 or 5%. Entering 5 would mean 500%, not 5%.

There is no optional basis argument. Do not append a fourth argument copied from another financial function. These examples use whole dates, positive discounts and positive model prices. Fractional date values and invalid-input behavior were not tested.

The independent column uses the actual-day model explained below. The application column preserves separately rounded values from the saved development-build output. Both columns are shown to twelve decimal places; intermediate reference calculations use exact rational arithmetic.

The two numerical columns deliberately preserve these differences. Inverting the comparison formula using the saved outputs gives implied day counts of 62, 91, 181, 181, 181, 4, 62 and 360, respectively. Those integers describe the observed results under that model; they do not prove the unavailable wrapper’s general date-count algorithm. The actual calendar counts are displayed separately.

In particular, the February 28 to March 1, 2024 interval is two actual days, while its saved yield implies four days in the comparison model. The two June/February-to-late-year cases produce the same saved result despite their different actual durations. These observations should remain visible when checking a workbook against a required quotation convention.

Set A2 to =DATE(1999;3;31), B2 to =DATE(1999;6;1) and C2 to 9.14%. In D2 enter =TBILLEQ(A2;B2;C2) and apply Percentage formatting. The documented example rounds to 9.4151%; retaining more digits gives the reference 9.415149356594%.

Keep A2 and B2 as dates rather than ambiguous strings such as 03/04/1999. The source Help demonstrates ISO-style text dates, but DATE makes the intended year, month and day visible without relying on locale-specific text recognition. The saved native checks used the direct DATE expressions in the table; this cell-based worksheet is an equivalent recipe, not a separately executed workbook.

For several bills, use one row per settlement, maturity and quoted discount. Keep the quoted discount and calculated yield in different, clearly labelled columns. A percentage-format change alone cannot convert one rate into the other.

For an explicitly actual-day comparison, let n be the actual number of days from settlement to maturity and d the decimal discount. An independent discount-price model per 100 repaid is:

price = 100 × (1 − d × n / 360)
holding return = (100 − price) / price
annualized simple yield = holding return × 365 / n
                       = 365 × d / (360 − d × n)

The 1999 dates are 62 days apart. The model gives a price of 98.425888888889 per 100, a discount amount of 1.574111111111, and a holding-period return of 0.015992856441. Annualizing that return by 365/62 gives 0.094151493566. These steps explain why the annual yield exceeds the quoted 9.14% discount.

With a face amount of 10,000, the same unrounded model gives a purchase price of 9842.588888888889 and a maturity gain of 157.411111111111. Do not round the price before calculating the reference yield if you want to reproduce the displayed precision. Actual transaction rounding is a separate input choice.

Two useful independent checks are available. First, invert the relationship with d = 360 × yield / (365 + n × yield); using the full-precision 62-day result recovers 0.0914. Second, at a 5% discount the 90-day reference is 0.051336146273, while the 181-day reference is 0.052001709645. The longer term produces a lower model purchase price and a slightly higher annualized simple yield.

This is simple annualization. It does not raise 1 + holding return to 365/n, and therefore should not be labelled an effective compounded annual return. This actual-day reconstruction matches three of the eight saved function results, including the Help example. It differs in the other five rows. It therefore serves as an independently specified comparison, not a claim to reproduce TBILLEQ universally.

Keep the input’s meaning clear. A discount quotation is not a purchase price, a coupon rate or the investor’s holding-period return. If the known input is an actual price instead of a discount, consult the separately documented TBILLYIELD function rather than putting that price into Discount.

The leap-year and month-end rows use their stated actual calendar differences only in the independent comparison column. The application’s differing results show that this replacement is not generally equivalent to TBILLEQ. The complete wrapper is unavailable, so the guide does not infer a universal date-count adjustment from eight observations.

The inspected registration confirms the three-argument identity, but the complete LibreOffice financial wrapper was not available. No precise native error code is asserted for reversed dates, dates outside the documented period, nonpositive discounts, fractional dates, or a nonpositive model denominator. Those inputs were not executed. Validate the intended dates and quotation before relying on a result, and preserve the original formula spelling when comparing imported workbooks.

TBILLPRICE, TBILLYIELD, DATE.

• Function-specific Help and the 1999 example
• Three-argument Analysis add-in registration
• LibreOffice 3.3 function appendix

The saved application is LibreOfficeDev 26.8.0.0.alpha0, build 2c87e51eeaa2b413ff4ae097b2705eea1995d8e5, on Linux. A deliberately stale cached control changed to 3 and an uncached control returned 7. Exact formula identities, result types and eight numerical observations were checked. This is headless import recalculation, with no stable-release or GUI test. The registration source is 26.8.1.1, which was not executed. The financial wrapper implementation was unavailable, so five actual-day discrepancies remain documented observations rather than a source-confirmed general algorithm.