Validation against published sources

What mortgagemath reproduces to the cent and the parameters that get you there

mortgagemath 0.7.0 · rendered 2026-05-06

Every fixture in the table below reproduces every value its source publishes, to the cent. The library follows a strict policy: if any published value diverges, the fixture stays out. The six parameter columns show the exact LoanParams settings required to match each source — the same six knobs documented in the at-a-glance vignette.

Validated fixtures

46 fixtures total.

Column codes. Day: 30/360 US residential, A/360 Actual/360 US commercial. Bal: RE round-each-balance, CP carry-precision. Rnd: UP ROUND_UP, DN ROUND_DOWN, HU ROUND_HALF_UP, HE ROUND_HALF_EVEN. Cmp: M monthly, j₂ semi-annual (Canadian Interest Act §6), A annual. Freq: M SM BW W Q A (monthly to annual). ARM: count of RateChange entries; cap indicates at least one payment_cap_factor. A dash is fully fixed-rate.

Bibliography

Arcones SOA FM §4.1 Ex 4. Arcones, M. A. Manual for SOA Exam FM / CAS Exam 2, Chapter 4 “Amortization and sinking bonds,” §4.1 Example 4. 2009. https://people.math.binghamton.edu/arcones/exam-fm/sect-4-1.pdf

BCC Brescia Italy. BCC di Brescia foglio informativo ‘Mutuo Fondiario Agrario Tasso Variabile Euribor’, Tipo Piano Francese, rata mensile for €200,000 at 5.65% over 10 years. https://www.bccbrescia.it/umbraco/surface/transparency/ShowFile/67119

Broverman MIC §2.1 Ex 2.7. Broverman, S. A. Mathematics of Investment and Credit, 8th ed., §2.1 Example 2.7(a)–(b). ACTEX, 2023. https://www.actexlearning.com/samples/MIC_8th_edition_051923_SAMPLE.pdf

CFPB H-25(B). Consumer Financial Protection Bureau. Closing Disclosure (Sample), Form H-25(B). 2014. https://files.consumerfinance.gov/f/201403_cfpb_closing-disclosure_cover-H25B.pdf

CFPB Interest-Only Loan. CFPB sample Loan Estimate for an Interest-Only loan. https://www.consumerfinance.gov/policy-compliance/guidance/mortgage-resources/tila-respa-integrated-disclosures/forms-samples/

eCampus §4.3 (Pearline / Erika / Johnetta). eCampus Ontario. Mathematics of Finance, §4.3 “Loan amortization: formula approach” (Example 4.3.1 Pearline; Exercises 2 Erika and 3 Johnetta). Pressbooks (CC-BY-NC-SA 4.0), 2023. https://ecampusontario.pressbooks.pub/financemath/chapter/4-3-loan-amortization-formula-approach/

eCampus §4.4.1 (T1 + renewal). eCampus Ontario. Mathematics of Finance, §4.4.1 “Mortgages: Formula approach.” Pressbooks (CC-BY 4.0). https://ecampusontario.pressbooks.pub/financemath/chapter/4-4-mortgages-formula-approach/

FNMA §1103. Federal National Mortgage Association. Multifamily Selling and Servicing Guide, §1103 “Actual/360 Tier 2 SARM Loan Amortization Calculation.” Effective 2026-04-03. https://mfguide.fanniemae.com/node/5286

FHLBB Review (March 1935). Federal Home Loan Bank Board. “Direct-Reduction Plan vs. Share-Accumulation Plan,” Federal Home Loan Bank Review, Vol. 1, No. 6 (March 1935), pp. 187–198. FRASER: https://fraser.stlouisfed.org/title/federal-home-loan-bank-review-116/march-1935-2083

Geltner Ch 20. Geltner, D., Miller, N. G., van de Minne, A., Eichholtz, P., Lindenthal, T., & Shen, J. Commercial Real Estate Analysis and Investments, online supplement Chapter 20: “Mortgage Basics II — Payments, Yields, and Values,” Exhibit 20-6 (Constant-Payment Mortgage). Routledge, 2024. ISBN 9781041081197.

Goldstein §10.3. Goldstein, L. J., Schneider, D. I., Lay, D. C., & Asmar, N. H. Finite Mathematics and Its Applications, 12th ed., §10.3 Example 1 + Table 1. Pearson, 2018. ISBN 978-0-13-443776-7. https://www.pearsonhighered.com/assets/samplechapter/0/1/3/4/0134437764.pdf

JHF Flat 35. Japan Housing Finance Agency (住宅金融支援機構) Flat 35 mortgage repayment comparison page. ¥20,000,000 at 1.5% fixed over 30 years, ganri kinto hensai (元利均等返済, equal total payment / standard annuity). https://www.flat35.com/hajimete/atoz/04.html

Las Positas §8.05. Las Positas College Mathematics. Math for Liberal Arts, §8.05 “Amortized Loans,” Examples 1 and 3. LibreTexts (CC-BY). https://math.libretexts.org/Courses/Las_Positas_College/Math_for_Liberal_Arts/08:_Consumer_Mathematics/8.05:_Amortized_Loans

LoanKeisan Japan. LoanKeisan.com. “3,000万円借入のローン計算、金利1.000％、借入期間30年.” Complete 360-row monthly amortization schedule. https://www.loankeisan.com/bin/calc?a=3000&b=0&i=1&p=30&t=r

MoneyVox Tableau d’amortissement. MoneyVox worked example of a tableau d’amortissement (French amortization schedule). €10,000 at 5% over 12 monthly payments with 0.35% assurance emprunteur. https://www.moneyvox.fr/credit/tableau-amortissement.php

MS State P3920. Mississippi State University Extension Service. Publication P3920, “Time Value of Money for Beginning Farmers and Ranchers.” https://extension.msstate.edu/sites/default/files/publications/P3920_web.pdf

Olivier Chans (T1 + renewal). Olivier, J. Business Math: A Step-by-Step Handbook, §13.4 “Special Application: Mortgages” (the Chans first term and renewal). LibreTexts (CC-BY-NC-SA), 2021. https://math.libretexts.org/Bookshelves/Applied_Mathematics/Business_Math_(Olivier)/13:_Understanding_Amortization_and_its_Applications/13.04:_Special_Application_-_Mortgages

OpenStax (Contemporary Mathematics). OpenStax College. Contemporary Mathematics, §6.8 “The Basics of Loans,” §6.12 “Renting and Homeownership,” and Chapter 6 Answer Key (problems 6.36, 6.78, 6.100, 6.110, 6.114). CC-BY-4.0. https://openstax.org/books/contemporary-mathematics

ProEducate ARM cap. ProEducate. ARM Payment Caps (worked example derived from a Federal Reserve consumer-handbook lineage, mirrored at mortgagesfinancingandcredit.org). 2014. https://www.proeducate.com/courses/Finance/PaymentCap.pdf

RBC Accelerated Bi-Weekly. RBC Accelerated Bi-Weekly mortgage worked example. https://www.rbcroyalbank.com/mortgages/accelerated-bi-weekly-payments.html

Reg Z H-14. U.S. Code of Federal Regulations. 12 CFR Part 1026 (Regulation Z, Truth in Lending), Appendix H, Sample H-14: Variable-Rate Mortgage Sample. https://www.ecfr.gov/current/title-12/chapter-X/part-1026/appendix-Appendix%20H%20to%20Part%201026

Skinner (1913). Skinner, E. B. The Mathematical Theory of Investment, §42 Examples 1 and 3. Boston: Ginn and Company, 1913. Public domain. https://archive.org/details/mathematicaltheo00skin

Solution Bank Italy. Solution Bank S.p.A. foglio informativo ‘Mutuo Fondario Prima Casa MCD’, Tipo Piano Francese, Giorni Commerciali / 360, rata mensile for €200,000 at 7% fixed over 30 years. https://solution.bank/wp-content/uploads/2024/06/Informazioni-Credito-Immobiliare-Consumatori-Mutuo-Fondario-Prima-Casa-MCD.pdf

Synthetic HALF_UP / ROUND_UP / HALF_EVEN. Synthetic boundary case constructed for this library: $100,001.25 / 4.8% / 30yr is engineered so month-1 unrounded interest equals exactly $400.005 — a half-cent boundary that distinguishes ROUND_HALF_UP ($400.01) from ROUND_HALF_EVEN ($400.00) and from ROUND_UP (which rounds the payment up to $524.68 instead of $524.67).

TI BA II Plus Guidebook. Texas Instruments. BA II PLUS Professional Calculator Guidebook, “Example: Computing Payments and Generating an Amortization Schedule.” https://education.ti.com/download/en/ed-tech/6D4382031E7640378E9B05B81AECBCF7/AB7F572CFF0447198598040876C89144/BAIIPlusProfessional_Guidebook_EN.pdf

Tistory Korean Mortgage. Korean mortgage blog worked example. ₩300,000,000 at 4.00% over 30 years, 원리금균등상환 (equal total payment / standard annuity). Publishes payment anchors for 10/20/30yr at 4.00% and 4.50%, plus the first 3 monthly rows at 4.00%/30yr. https://jjonew.tistory.com/entry/2025%EB%85%84-%EC%A3%BC%ED%83%9D%EB%8B%B4%EB%B3%B4%EB%8C%80%EC%B6%9C-3%EC%96%B5-%EC%9B%94-%EC%83%81%ED%99%98%EA%B8%88%EC%9D%80-%EC%96%BC%EB%A7%88%EC%9D%BC%EA%B9%8C-%EA%B8%88%EB%A6%AC%EB%B3%84-%EC%8B%A4%EC%A0%84-%EB%B9%84%EA%B5%90%ED%91%9C-%F0%9F%93%8A

Wikipedia mortgage calc. Wikipedia contributors. “Mortgage calculator.” Wikipedia, The Free Encyclopedia. Worked example in the monthly-payment formula section. https://en.wikipedia.org/wiki/Mortgage_calculator

Zero-Interest Promotional Financing. Synthetic fixture modeling 0% APR promotional financing (e.g. consumer electronics or furniture loans).