{"uid":"cap_70jiSQChvp_B-GUeQYaRT","slug":"loan-amortization-calculator-coprocesseur-d-terministe-91a97965","name":"Loan Amortization Calculator (Coprocesseur Déterministe)","description":"Trois calculs déterministes destinés aux agents IA : amortissement de prêt, distance orthodromique, conversion d'unités.\n\nChaque réponse porte son résultat, la formule appliquée, ses limites, et une empreinte SHA-256 recalculable — la chaîne exacte qui a été hachée est renvoyée avec, et `POST /verifier` permet de la contrôler gratuitement. Un même appel rend toujours la même empreinte : l'horodatage est exclu du hachage.\n\nLe paiement suit le protocole x402 (version 2), en USDC sur Base.","url":"https://x402.laboiteatubes.media/amortissement?utm_source=zero.xyz","method":"GET","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method"],"properties":{"type":{"type":"string","const":"http"},"method":{"enum":["GET"],"type":"string"},"queryParams":{"type":"object","required":["montant","taux_annuel","duree_mois"],"properties":{"montant":{"type":"number","maximum":1000000000,"minimum":0.01},"duree_mois":{"type":"integer","maximum":600,"minimum":1},"taux_annuel":{"type":"number","maximum":100,"minimum":0}}}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object"}}}}},"responseSchema":{"type":"json","example":{"notes":["Calcul mené en centimes entiers, arrondi au centime le plus proche à chaque échéance.","La dernière échéance est ajustée pour solder exactement le capital.","Taux nominal proportionnel (t/12). Ce n'est ni un TAEG ni un taux actuariel : assurance, frais de dossier et garanties ne sont pas inclus."],"preuve":{"note":"L'horodatage `calcule_le` est volontairement exclu de l'empreinte.","empreinte":"14be0ebc8d16f4fc4a5cc3884f0a624365a7d468612e9098b0fbc66ae799c673","algorithme":"SHA-256","chaine_hachee":"{\"entrees\":{\"devise\":\"EUR\",\"duree_mois\":2,\"montant\":200000,\"taux_annuel\":3.5},\"formule_expression\":\"M = C × i / (1 − (1 + i)^(−n)),  avec i = t/1200\",\"operation\":\"amortissement\",\"resultat\":{\"cout_total_credit\":875.42,\"derniere_echeance\":100437.71,\"echeancier\":[{\"capital_rembourse\":99854.38,\"capital_restant_du\":100145.62,\"echeance\":100437.71,\"interets\":583.33,\"mois\":1},{\"capital_rembourse\":100145.62,\"capital_restant_du\":0,\"echeance\":100437.71,\"interets\":292.09,\"mois\":2}],\"mensualite\":100437.71,\"nombre_echeances\":2,\"taux_mensuel\":0.0029166667,\"total_rembourse\":200875.42},\"version_formule\":\"amortissement-mensualites-constantes@1.0.0\"}","champs_couverts":["operation","version_formule","entrees","resultat","formule_expression"],"canonicalisation":"JSON à clés triées récursivement, sans espace, encodé en UTF-8"},"entrees":{"devise":"EUR","montant":200000,"duree_mois":2,"taux_annuel":3.5},"formule":{"reference":"Formule standard de l'annuité constante (valeur actuelle d'une suite d'annuités).","variables":{"C":"capital emprunté","M":"mensualité constante","i":"taux périodique mensuel","n":"nombre de mensualités","t":"taux annuel nominal en %"},"expression":"M = C × i / (1 − (1 + i)^(−n)),  avec i = t/1200","description":"Prêt à mensualités constantes (amortissement dit « français »). Les intérêts de chaque échéance sont calculés sur le capital restant dû ; le solde de la mensualité amortit le capital."},"service":"coprocesseur-deterministe","resultat":{"echeancier":[{"mois":1,"echeance":100437.71,"interets":583.33,"capital_rembourse":99854.38,"capital_restant_du":100145.62},{"mois":2,"echeance":100437.71,"interets":292.09,"capital_rembourse":100145.62,"capital_restant_du":0}],"mensualite":100437.71,"taux_mensuel":0.0029166667,"total_rembourse":200875.42,"nombre_echeances":2,"cout_total_credit":875.42,"derniere_echeance":100437.71},"operation":"amortissement","calcule_le":"2026-08-16T08:29:39.319Z","version_formule":"amortissement-mensualites-constantes@1.0.0","version_service":"1.0.0"}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_aDY3wBB-C_metdzliA15F","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes a complete French-style constant-payment loan amortization schedule, including monthly payment, total cost of credit, and a full repayment table, with a SHA-256 proof of the result.","exampleAgentPrompt":"Can you calculate the full amortization schedule for a 150,000 EUR loan at an annual rate of 4.5% over 240 months, showing monthly payments and how much goes to interest vs. principal each month?","exampleUseCases":[{"title":"Mortgage feasibility check","prompt":"I'm considering a 300,000 EUR home loan at 3.8% annual interest over 300 months — what would my monthly payment be and what's the total I'd end up repaying?"},{"title":"Car loan comparison","prompt":"I'm looking at a 25,000 EUR car loan at 5.2% per year over 60 months. Can you show me the full repayment schedule month by month so I know exactly what I'm paying in interest vs. principal?"},{"title":"Verifiable loan audit for agent pipeline","prompt":"Compute the amortization for a 500,000 EUR loan at 2.9% annual rate over 360 months and give me the SHA-256 proof hash so I can verify the result hasn't been tampered with."}],"resultDescription":"Returns a JSON object with the computed monthly payment (mensualite), total amount repaid, total credit cost, the full month-by-month amortization table (each row showing interest paid, principal repaid, and remaining balance), plus a SHA-256 cryptographic proof covering all inputs and outputs — along with the exact canonical string that was hashed so the result can be independently verified.","failureModes":["Missing required parameters (montant, taux_annuel, or duree_mois) returns a 400 error","montant outside range 0.01–1,000,000,000 is rejected","duree_mois outside range 1–600 is rejected","taux_annuel outside range 0–100 is rejected","Payment not provided or invalid x402 payment header results in 402 Payment Required","Network timeout or upstream unavailability returns a 5xx error"],"whenToPreferThis":"Choose this endpoint when you need a deterministic, cryptographically verifiable loan amortization calculation — especially in agentic pipelines where auditability matters. The SHA-256 proof makes results independently verifiable without re-calling the API. Prefer this over general-purpose calculators when you need the exact canonical French-style (mensualités constantes) amortization method, a full month-by-month schedule, and confidence that the same inputs always produce the same hash.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-13T14:08:33.807Z","isFirstParty":false,"canonicalSlug":"loan-amortization-calculator-coprocesseur-d-terministe-91a97965"}