# Loan Amortization Calculator (Coprocesseur Déterministe)

> Loan Amortization Calculator (Coprocesseur Déterministe) is a paid API for AI agents from x402.laboiteatubes.media, paid per call via x402, $0.003/call, status unknown (last checked 2026-10-13).

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.

## Facts

- Endpoint: GET https://x402.laboiteatubes.media/amortissement?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-13
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/loan-amortization-calculator-coprocesseur-d-terministe-91a97965
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_70jiSQChvp_B-GUeQYaRT

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability loan-amortization-calculator-coprocesseur-d-terministe-91a97965
```

Example prompt: 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?

## When to prefer this

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.

## Known failure modes

- 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

## How this service works

Trois calculs déterministes destinés aux agents IA : amortissement de prêt, distance orthodromique, conversion d'unités.

Chaque 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.

Le paiement suit le protocole x402 (version 2), en USDC sur Base.

## Output

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.

## Request schema (JSON Schema)

```json
{
 "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"
    }
   }
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "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": 2
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/loan-amortization-calculator-coprocesseur-d-terministe-91a97965/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from x402.laboiteatubes.media](https://www.zero.xyz/host/x402.laboiteatubes.media/llms.txt)