{ "category": "Financial functions", "display_name": "PMT", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.PMT", "implementation_state": { "answer_bank": { "excel_builds": [ "20131", "20228", "20527", "?" ], "larger_numeric": 0, "last_bit": 151, "matched": 291827, "other_mismatch": 0, "refused": 0, "rows": 291978, "unread": 0, "worst_ulp": 4 }, "detail": "Everything else matches (291,978 in the answer bank and 9 workbook cells). Last-bit means a finite number within 16 ULP of Excel's.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "close", "state_label": "Close: last-bit deviations remain", "summary": "Close: 151 of 291,987 recorded answers differ in the last bits, worst 4 ULP", "workbook_corpus": { "cells": 9, "matched": 9 } }, "implementations": [ { "commit": "9e1884369a678158dd82d3d74188daf986995e87", "flavour": "excel-compatibility-candidate", "language": "Rust", "name": "CalcFunc", "own_code": [ "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/financial.rs#L172-L175" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/financial::tv_out", "catalogue/financial::timing", "ported/excel_numeric::backend::sqrt", "ported/excel_numeric::binary_with", "ported/excel_numeric::asuint64", "ported/excel_numeric::asdouble", "ported/excel_numeric::top16", "ported/excel_numeric::excel_expm1_spilled", "ported/excel_numeric::expm1_internal_graph", "ported/excel_numeric::excel_pow_positive", "ported/excel_numeric::excel_pow_chain", "ported/excel_numeric::excel_x87_add", "ported/excel_numeric::excel_x87_sub", "ported/excel_numeric::excel_x87_mul", "ported/excel_numeric::excel_x87_div", "ported/excel_numeric::excel_x87_recip", "ported/excel_numeric::log_general_hi_lo", "ported/excel_numeric::excel_log1p", "ported/excel_numeric::excel_log1p_atanh", "ported/excel_numeric/x87::mul", "ported/excel_numeric/x87::add", "ported/excel_numeric/x87::sub", "ported/excel_numeric/x87::div", "ported/excel_numeric/x87::recip", "ported/excel_numeric/x87_chains::pow2_positive", "ported/excel_numeric/x87_chains::pow2", "ported/excel_numeric/x87_chains::exp_ext", "ported/excel_numeric/x87_chains::exp_with", "ported/excel_numeric/x87_chains::excel_exp", "ported/excel_numeric/x87_chains::log_with", "ported/excel_numeric/x87_chains::excel_log", "ported/financial_time_value_family::PaymentTiming::factor", "ported/financial_time_value_family::validate_finite", "ported/financial_time_value_family::growth", "ported/financial_time_value_family::annuity_term", "ported/financial_time_value_family::balance_equation", "ported/financial_time_value_family::pmt", "ported/financial_time_value_family::values_bracket_root", "ported/financial_time_value_family::bisect_rate_bracket", "ported/financial_time_value_family::search_rate_bracket_from_zero", "ported/financial_time_value_family::rate", "ported/financial_time_value_family::polish_root", "ported/financial_time_value_family::rate_root", "ported/power_fn::exact_integer_magnitude", "ported/power_fn::accept_negative_base_odd_root", "ported/power_fn::binexp_positive", "ported/power_fn::power_kernel" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/financial.rs#L172-L175", "state": "close", "suite": null, "summary": "Close: 151 of 291,987 recorded answers differ in the last bits, worst 4 ULP" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.PMT.json", "name": "PMT", "notes": [ { "basis": "For each of 1,184 rates one binary64 L reproduces Excel's em at every nper (1,622 of 1,622 power-of-two and 1,849 of 1,849 other nper, L taken from nper 1 alone). The series gives that L at 1,181 rates; the correctly rounded log1p and fdlibm's log1p each give it at 667. Order and precision of the last two steps: in all 4,802 groups of recorded answers sharing (rate, nper) with 8 or more pv values, these steps admit one em; a binary64 quotient leaves 59 groups with none, and binary64 for both steps 111. 720 of 720 fresh type 0 rows over 20 rates, both signs, match (Excel build 20527). Over every recorded PMT row, types and fv included, 279,887 of 291,978 match.", "documentation": null, "evidence": [ { "commit": "b5d84a80a5a4640eca9ce04f232c0bc115503f34", "locator": "section UPDATE", "note": "research write-up; the update supersedes the blocked outcome at its head", "path": "content/notes/evidence/2026-11-04/annuity-EVIDENCE.txt", "repository": "ExcelFunctionsHandbook" }, { "commit": "08ea3d7ae0ba8d7241e2545aeeb78ff246ac6963", "locator": "pmt", "note": "the logarithm and the stored quotient in the product; the commit message carries the row counts", "path": "crates/calc-func/src/ported/financial_time_value_family.rs", "repository": "DnaCalc" }, { "commit": "08ea3d7ae0ba8d7241e2545aeeb78ff246ac6963", "locator": "excel_log1p_atanh", "note": "the series", "path": "crates/calc-func/src/ported/excel_numeric/mod.rs", "repository": "DnaCalc" }, { "commit": "c9f9d354165d2c20b9455c32582ea50baac7ba73", "locator": null, "note": "recorded answers of the 30-year loan block", "path": "crates/calc-func/tests/captures/catalogue/sections/dcj9k_annuity.capture.json", "repository": "DnaCalc" } ], "functions": [ "FUNC.PMT" ], "inferred": "The range -1/3 to 1/2 is where twelve series terms converge, not a measured Excel boundary. Rate 0.419, near sqrt(2)-1, misses by 1 unit, so a range reduction may start there. Negative rates rest on 20 rates' controls and the recorded rows.", "kind": "bit-matching-detail", "note_id": "FN-PMT-001", "open": [ "type 1: Excel multiplies q by one stored binary64 K near rate/(1+rate) per rate (pinned at all but one of about 458 recorded rates and at 20 of 20 fresh ones), but K's formula is open: the correctly rounded quotient fits 344 of 458.", "Nonzero fv: the numerator of q is open. The best form tried fits 5,600 of 7,491 rows, and 146 rows admit no binary64 numerator under this order.", "Rates outside -1/3 to 1/2." ], "recorded_on": "2026-11-04", "repros": [ { "call": "=PMT(0.05/12,360,200000)", "correct": { "bits": "0xc090c692af15f639", "display": "-1073.643246024278", "how": "mpmath at 800 bits with rate the binary64 0x3f71111111111111 that 0.05/12 evaluates to; correctly rounded.", "kind": "number" }, "excel": { "bits": "0xc090c692af15f63a", "display": "-1073.6432460242781", "kind": "number" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "source": { "commit": "c9f9d354165d2c20b9455c32582ea50baac7ba73", "locator": "sheet dcj9k_annuity, row 726, column 4", "note": null, "path": "crates/calc-func/tests/captures/catalogue/sections/dcj9k_annuity.capture.json", "repository": "DnaCalc" } } ], "schema": "efh.function-note/v1", "statement": "With RN(v) meaning v rounded to 64 bits on the x87 unit and then stored to binary64, PMT with fv 0 and type 0 at rates from -1/3 to 1/2 runs: s = rate/(2+rate); L = 2s + 2s*(s^2*T), where T = 1/3 + s^2/5 + ... + s^20/23 by Horner, all in plain binary64, which is the atanh series for ln(1+rate) (Abramowitz and Stegun 4.1.27) with the 2s term added last; t = -(nper*L); u = exp(t) stored; em = RN(RN(RN(u-1)*t)/ln(u)) for |t| < 1, and RN(u-1) otherwise, Kahan's way of forming expm1; q = RN(pv/em); PMT = RN(q*rate). L is not the correctly rounded logarithm: at rate 0.05/12 it is 0x3f7107fd59addc8a, one unit below 0x3f7107fd59addc8b, and the common 30-year loan below comes out 1 unit from the correctly rounded payment.", "status": "measured", "title": "PMT takes ln(1+rate) from a series, and stores its quotient before the rate" }, { "basis": "Twelve recorded periods of one loan, read from the catalogue capture, compared with exact values and with Excel's own PMT and IPMT by binary64 subtraction, recomputed for this note.", "documentation": null, "evidence": [ { "commit": "b5d84a80a5a4640eca9ce04f232c0bc115503f34", "locator": null, "note": "research write-up; finding F4 gives 4 and 8 of 12 periods, and the capture gives the 2 and 7 stated here", "path": "content/notes/evidence/2026-11-04/annuity-EVIDENCE.txt", "repository": "ExcelFunctionsHandbook" }, { "commit": "c9f9d354165d2c20b9455c32582ea50baac7ba73", "locator": null, "note": "recorded answers of the 30-year loan block", "path": "crates/calc-func/tests/captures/catalogue/sections/dcj9k_annuity.capture.json", "repository": "DnaCalc" } ], "functions": [ "FUNC.PMT", "FUNC.PPMT" ], "inferred": null, "kind": "excel-differs-from-math", "note_id": "FN-PPMT-001", "open": [], "recorded_on": "2026-11-04", "repros": [ { "call": "=PPMT(0.05/12,1,360,200000)", "correct": { "bits": "0xc06e09eace05071f", "display": "-240.30991269094463", "how": "mpmath at 800 bits with rate the binary64 0x3f71111111111111 that 0.05/12 evaluates to; correctly rounded.", "kind": "number" }, "excel": { "bits": "0xc06e09eace050723", "display": "-240.30991269094474", "kind": "number" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "source": { "commit": "c9f9d354165d2c20b9455c32582ea50baac7ba73", "locator": "sheet dcj9k_annuity, row 727, column 4", "note": null, "path": "crates/calc-func/tests/captures/catalogue/sections/dcj9k_annuity.capture.json", "repository": "DnaCalc" } } ], "schema": "efh.function-note/v1", "statement": "On the 30-year loan PPMT(0.05/12,k,360,200000), for k from 1 to 12 every PPMT answer is 3 to 5 units above the correctly rounded principal payment, while PMT is 1 unit away. Excel's own answers do not satisfy the identity: in binary64, PMT - IPMT equals PPMT in 2 of the 12 periods and PMT - PPMT equals IPMT in 7. So reproducing PPMT from PMT and IPMT misses the last bits. FN-IPMT-001 gives the route Excel takes instead.", "status": "measured", "title": "PPMT is not PMT minus IPMT, and sits further from the exact value than PMT" } ], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n[IPMT](FUNC.IPMT.md) and [PPMT](FUNC.PPMT.md) split interest and principal; [PV](FUNC.PV.md) and [FV](FUNC.FV.md) solve for a balance; [RATE](FUNC.RATE.md) solves for the periodic rate.\n\n\n\n\n", "how-to-implement": "\nThe following is the current **type-zero positive-rate discount route**, with the recovered logarithm series used on `-1/3<=rate<=1/2`. The series reproduces 1,181 of 1,184 inferred logarithm values in the note; it still has exceptions inside that range. Its negative-rate and outer-domain limitations are stated below. Let `D(op)` mean ordinary binary64 round-to-nearest/even, and `R(op)` the [stored 64-bit-significand operation](../model/09-staged-arithmetic.md).\n\n1. Reject zero periods with `#NUM!`. At exactly `r=0`, return `-(pv+fv)/n`. Otherwise reject a growth base `1+r<=0`.\n2. Form `s=D(r/D(2+r))`, `s2=D(s*s)`. Start `T=D(1/23)`. For `k=10` down to `1`, assign `T=D(D(T*s2)+D(1/(2*k+1)))`. Form `a=D(2*s)` and `L=D(a+D(a*D(s2*T)))`. This is a twelve-term atanh expansion, **not** a correctly rounded log1p call.\n3. Store `t=-D(n*L)`. Obtain the measured public exponential `u=EXP(t)`. If `u==1`, let `em=t`. Otherwise set `d=R(u-1)`; for `abs(t)<1`, use `em=R(R(d*t)/LN(u))`, where LN is the measured public stored result; otherwise use `em=d`. Reject zero or nonfinite em with `#NUM!` before division. This Kahan correction avoids cancellation in `exp(t)-1`.\n4. On the positive-rate, positive-period discount arm (`t<0`), form `b=R(pv+fv)`, `q=R(R(b/em)+fv)`, and return `R(q*r)` for type zero. Each addition and the division is a separate store. With `fv=0` this reduces to quotient first, rate last.\n\nWorked zero-future-value case, `r=0.25,n=1,pv=1000`: the stated reconstruction gives the following binary64 values. The stored correction moves `em` one representable step from the direct subtraction.\n\n| Stage | Value | Bits |\n|---|---:|---|\n| Series logarithm `L` | `0.22314355131420974` | `0x3fcc8ff7c79a9a21` |\n| `t=-n*L` | `-0.22314355131420974` | `0xbfcc8ff7c79a9a21` |\n| Stored EXP `u` | `0.8` | `0x3fe999999999999a` |\n| Direct difference `d` | `-0.19999999999999996` | `0xbfc9999999999998` |\n| Corrected difference `em` | `-0.19999999999999998` | `0xbfc9999999999999` |\n| Balance quotient `q` | `-5000` | `0xc0b3880000000000` |\n| Payment | `-1250` | `0xc093880000000000` |\n\nWith the same rate, period and principal but `fv=250`, the first stored balance is `1250`. Dividing by em and then adding 250 gives `q=-6000.000000000001`; the final payment is `-1500.0000000000002`. An algebraic one-period calculation rounds differently. These are worked evaluations of the reconstruction, not additional Excel captures.\n\nThe nonzero-future-value discount fold is supported by 192 paired calls in the current source; 60 and 99 separately selected readings distinguish its two additions. This later result supersedes that part of the older note's open list. The common loan `PMT(0.05/12,360,200000)` has recorded result `-1073.6432460242781` in FN-PMT-001; replaying the stated series and stored quotient also gives that value.\n\nThe later R31 source also isolates the **negative-rate type-zero balance fold**. For a valid negative rate and finite nonzero em, use the same `b=R(pv+fv)`, `q=R(R(b/em)+fv)`, `payment=R(q*r)` stores. Its source records 192 paired future-value calls for that rate sign, 84 and 114 ties for the two additions, and 32 independently measured final-product ties. This closes that composition stage; it does not make the logarithm or every route exact.\n\nWorked negative-rate composition: `r=-0.25,n=1,pv=1000,fv=250`. The series gives `L=-0.2876820724517809`, t is positive and stored EXP is `1.3333333333333333`. The correction changes the direct difference `0.33333333333333326` to em `0.3333333333333333`. The stored balance is 1250, q is 4000 and payment is `-1000`. These are reconstruction values, not new Excel readings. The interactive calculator is pinned separately and can predate this later source update.\n\nThe positive-rate code separately handles opposite equal balances as interest-only. Negative-rate calls now retain the common stored fold instead. Rates outside the series’ chosen convergence range, its in-range exceptions and remaining last-bit cases are not solved by this recipe. The note retains an in-range exception at rate `0.419`; a global reduction boundary has not been identified. The series range is an implementation choice, not a measured global Excel boundary. The current type-one coefficient has its own measured stores; it must not be folded into the type-zero recipe by algebra alone. The old annuity write-up’s initial “blocked” section is superseded by its update and later code.\n\n\n", "quirks": "\nCash inflows and outflows have opposite signs. A monthly payment needs a monthly rate and a count of months. Taxes and fees are outside this formula. Exactly zero rate has a separate linear branch; a merely small rate must retain the discount computation. Zero periods and invalid growth domains need error handling.\n\n\n", "sources": "\n- [Microsoft: PMT function](https://support.microsoft.com/en-us/excel/functions/pmt-function), opened 6 November 2026; syntax, documented argument rules and errors.\n- [DnaCalc implementation](https://github.com/DnaCalc/DnaCalc/blob/481f4ab85d3bf5a95b6daf959bb75ccb2f8b40f8/crates/calc-func/src/ported/financial_time_value_family.rs); implementation steps and the limits identified in the text.\n- [Annuity research, including the superseding update](../notes/evidence/2026-11-04/annuity-EVIDENCE.txt).\n- [Logarithm and cancellation correction](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/crates/calc-func/src/ported/excel_numeric/mod.rs).\n- [R31 negative-rate controls](https://github.com/DnaCalc/DnaCalc/blob/481f4ab85d3bf5a95b6daf959bb75ccb2f8b40f8/crates/calc-func/tests/f3_financial.rs); retained paired-balance and final-product controls.\n\n", "try-it": "\n`=PMT(0,4,1000)` returns `-250`: four equal outflows repay a positive principal. `=PMT(0.25,1,1000,0,0)` is about `-1250`, repaying the principal and one period’s interest.\n\n\n", "version-differences": "The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.\n\n| Excel 16.0 build | Platform and CPU | Captured inputs |\n|---|---|---:|\n| 19929 | Windows, bitness not recorded, CPU not recorded | 47 |\n| 20131 | Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics | 289,642 |\n| 20228 | Windows, 64-bit, CPU not recorded | 2,076 |\n\nThe record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.\n\n[Recorded environments and comparison details](https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.PMT.json).\n\nRetained controls from the indexed captures:\n\n| Build and recorded CPU | Captured call or arguments | Excel result |\n|---|---|---|\n| 20131, AMD Ryzen 7 4800H with Radeon Graphics | [`PMT(0.1,1,1000,0,0)`](https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/cache/oracle/build-20131/PMT.jsonl.gz) | `-1100.0000000000002` (`0xc091300000000001`) |\n| 20228, CPU not recorded | [`PMT(0.0649385261097155,17,1567.723775140197,0,0)`](https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/work/w109/G6-cumprinc/answers-pmt-cumprinc-companion-20260809.json.gz) | `-154.99052913979685` (`0xc0635fb26a2aa533`) |\n\nThese are earlier recorded answers, not new Excel runs or an additional cross-build comparison. The function JSON retains each source locator, exact argument bits where available, and input-route status. Call notation does not imply that captured binary64 values were entered as decimal formula literals.", "what-it-does": "\n`PMT(rate, nper, pv, [fv], [type])` returns a fixed payment at a constant rate over equal periods. `fv` defaults to zero. Type zero (the default) pays at period end; type one pays at the beginning. Use a rate per payment period.\n\n\n" }, "signature": { "display": "PMT(rate, nper, pv, [fv], [type])", "parameters": [ { "description": null, "name": "rate", "optional": false, "repeats": false }, { "description": null, "name": "nper", "optional": false, "repeats": false }, { "description": null, "name": "pv", "optional": false, "repeats": false }, { "description": null, "name": "fv", "optional": true, "repeats": false }, { "description": null, "name": "type", "optional": true, "repeats": false } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 5, "min": 3 }, "category": "Financial functions", "classification": { "arg_preparation_profile": "RefsVisibleInAdapter", "coercion_lift_profile": "Custom", "determinism_class": "Deterministic", "error_collapse_profile": "None", "fec_dependency_profile": "None", "host_interaction_class": "None", "kernel_signature_class": "Custom", "rich_value_usage": "RichBlind", "surface_fec_dependency_profile": "RefOnly", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": "Fixed payment per period that pays off a loan at a fixed rate", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the periodic payment for an annuity", "microsoft_url": "https://support.microsoft.com/en-us/office/pmt-function-0214da64-9a63-4996-bc20-214433fa6441" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "PMT" }, { "locale": "bg-BG", "name": "PMT" }, { "locale": "cs-CZ", "name": "PMT" }, { "locale": "da-DK", "name": "YDELSE" }, { "locale": "de-DE", "name": "RMZ" }, { "locale": "el-GR", "name": "PMT" }, { "locale": "en-AU", "name": "PMT" }, { "locale": "en-GB", "name": "PMT" }, { "locale": "en-US", "name": "PMT" }, { "locale": "es-ES", "name": "PAGO" }, { "locale": "et-EE", "name": "PMT" }, { "locale": "fi-FI", "name": "MAKSU" }, { "locale": "fr-FR", "name": "VPM" }, { "locale": "he-IL", "name": "PMT" }, { "locale": "hr-HR", "name": "PMT" }, { "locale": "hu-HU", "name": "RÉSZLET" }, { "locale": "id-ID", "name": "PMT" }, { "locale": "it-IT", "name": "RATA" }, { "locale": "ja-JP", "name": "PMT" }, { "locale": "ko-KR", "name": "PMT" }, { "locale": "lt-LT", "name": "PMT" }, { "locale": "lv-LV", "name": "PMT" }, { "locale": "nb-NO", "name": "PMT" }, { "locale": "nl-NL", "name": "BET" }, { "locale": "pl-PL", "name": "PMT" }, { "locale": "pt-BR", "name": "PGTO" }, { "locale": "pt-PT", "name": "PGTO" }, { "locale": "ro-RO", "name": "PMT" }, { "locale": "ru-RU", "name": "ПЛТ" }, { "locale": "sk-SK", "name": "PMT" }, { "locale": "sl-SI", "name": "PMT" }, { "locale": "sr-Latn-RS", "name": "PMT" }, { "locale": "sv-SE", "name": "BETALNING" }, { "locale": "th-TH", "name": "PMT" }, { "locale": "tr-TR", "name": "FAİZ_ORANI" }, { "locale": "uk-UA", "name": "PMT" }, { "locale": "vi-VN", "name": "PMT" }, { "locale": "zh-CN", "name": "PMT" }, { "locale": "zh-HK", "name": "PMT" }, { "locale": "zh-TW", "name": "PMT" } ], "signature": { "display": "PMT(rate, nper, pv, [fv], [type])", "parameters": [ { "description": null, "name": "rate", "optional": false, "repeats": false }, { "description": null, "name": "nper", "optional": false, "repeats": false }, { "description": null, "name": "pv", "optional": false, "repeats": false }, { "description": null, "name": "fv", "optional": true, "repeats": false }, { "description": null, "name": "type", "optional": true, "repeats": false } ], "trailing_repeats": false }, "surface_name": "PMT", "version_marker": null, "xlcall": { "code": "59", "symbol": "xlfPmt" } }, "microsoft": "https://support.microsoft.com/en-us/office/pmt-function-0214da64-9a63-4996-bc20-214433fa6441" }, "try_it": { "formula": "=PMT(0.25,1,1000,0,0)" }, "url": "https://handbook.dnacalc.com/functions/PMT.html", "variants": [], "versions": [ { "behaviour": "=PMT(0.05/12,360,200000) returned -1073.6432460242781 (0xc090c692af15f63a). Inputs were supplied through formula literals. These are controls from this environment, not a same-input comparison with another build.", "excel_build": "16.0.20527.20088", "observations": [ { "call": "=PMT(0.05/12,360,200000)", "excel": { "bits": "0xc090c692af15f63a", "display": "-1073.6432460242781", "kind": "number" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA" } ], "platform": "Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/3345a87/content/notes/FN-PMT-001.json" ] }, { "behaviour": "47 captured inputs are indexed for this environment. Capture dates are not recorded. This is a reading count, not a comparison with another build.", "excel_build": "16.0 build 19929", "platform": "Windows, bitness not recorded, CPU not recorded", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.PMT.json" ] }, { "behaviour": "289,642 captured inputs are indexed for this environment. Capture dates: 2026-07-11 to 2026-07-23. This is a reading count, not a comparison with another build. Retained control PMT(0.1,1,1000,0,0) returned -1100.0000000000002 (0xc091300000000001). The selected archive row does not record its input plumbing; no input route is inferred.", "excel_build": "16.0 build 20131", "observations": [ { "call": "PMT(0.1,1,1000,0,0)", "excel": { "bits": "0xc091300000000001", "display": "-1100.0000000000002", "kind": "number" }, "input_route": "not-recorded", "inputs": [ { "name": "argument1", "value": { "bits": "0x3fb999999999999a", "display": "0.1", "kind": "number" } }, { "name": "argument2", "value": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" } }, { "name": "argument3", "value": { "bits": "0x408f400000000000", "display": "1000", "kind": "number" } }, { "name": "argument4", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } }, { "name": "argument5", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20131, Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics.", "source": { "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2", "locator": "PMT|0x3fb999999999999a|0x3ff0000000000000|0x408f400000000000|0x0000000000000000|0x0000000000000000", "path": "cache/oracle/build-20131/PMT.jsonl.gz", "repository": "CalcFunc-Evidence" } } ], "platform": "Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.PMT.json", "https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/cache/oracle/build-20131/PMT.jsonl.gz" ] }, { "behaviour": "2,076 captured inputs are indexed for this environment. Capture dates: 2026-08-09 to 2026-08-09. This is a reading count, not a comparison with another build. Retained control PMT(0.0649385261097155,17,1567.723775140197,0,0) returned -154.99052913979685 (0xc0635fb26a2aa533). The capture specifies exact-double bulk Value2 cell input.", "excel_build": "16.0 build 20228", "observations": [ { "call": "PMT(0.0649385261097155,17,1567.723775140197,0,0)", "excel": { "bits": "0xc0635fb26a2aa533", "display": "-154.99052913979685", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "argument1", "value": { "bits": "0x3fb09fcfade4447f", "display": "0.0649385261097155", "kind": "number" } }, { "name": "argument2", "value": { "bits": "0x4031000000000000", "display": "17", "kind": "number" } }, { "name": "argument3", "value": { "bits": "0x40987ee5254f7337", "display": "1567.723775140197", "kind": "number" } }, { "name": "argument4", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } }, { "name": "argument5", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20228, Windows, 64-bit, CPU not recorded.", "source": { "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2", "locator": "cumx-c00-t0-v00-pmt", "path": "work/w109/G6-cumprinc/answers-pmt-cumprinc-companion-20260809.json.gz", "repository": "CalcFunc-Evidence" } } ], "platform": "Windows, 64-bit, CPU not recorded", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.PMT.json", "https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/work/w109/G6-cumprinc/answers-pmt-cumprinc-companion-20260809.json.gz" ] } ] }