{
  "address": "91bcf29a82898933ec2fdb47abaa0fa2",
  "category": "other",
  "question": "What is the fixed monthly payment on a $200000 loan at 6% annual interest amortized over 360 months?",
  "answer": "$1,199.10",
  "askedBy": {
    "kind": "guest",
    "display": "method deck",
    "stamped": false,
    "id": null
  },
  "answeredBy": "method",
  "madeAt": "2026-09-30T22:39:30.722Z",
  "validUntil": null,
  "validityClass": "forever",
  "sources": [
    {
      "label": "Principles of Corporate Finance",
      "url": null
    }
  ],
  "supersedes": null,
  "supersededBy": null,
  "isSeed": false,
  "seedSource": null,
  "seedAttribution": null,
  "duplicateOfQid": null,
  "publishedAt": null,
  "unpublishedAt": null,
  "voteCount": 0,
  "queuedForSubstrate": false,
  "answerMethod": "method",
  "unsourced": false,
  "source": {
    "kind": "edition_page",
    "value": "Brealey, Myers, Allen, Principles of Corporate Finance, 13th ed., Chapter 3, section 3-3 (Loan Amortization)",
    "retrieved_utc": "2026-09-30T19:31:29Z"
  },
  "qsha256": "4a7d786225319bd55a9aa8873e210a1bde3e1599f7a557c7017788d75dba8118",
  "runOne": null,
  "cardContractVersion": "card_contract/1",
  "deck_id": "method-deck",
  "deck_title": "Method Deck",
  "method": {
    "name": "Amortized loan payment",
    "version": "1",
    "source_url_or_file": "methods/loan-payment-amortized.cjs",
    "sha256_of_method_file": "28032747da12557a7998f049ff904087501f4a0c6c544f5aeedcceca02f52b7b"
  },
  "receipt": {
    "inSubstrate": false,
    "local": true,
    "modelCallsAtMint": 0,
    "tokensAtMint": 0
  },
  "method_deck": {
    "inputs": [
      {
        "name": "principal",
        "type": "number",
        "unit": "currency units",
        "required": true,
        "description": "Loan amount borrowed",
        "min": 0
      },
      {
        "name": "annual_rate_percent",
        "type": "number",
        "unit": "%",
        "required": true,
        "description": "Nominal annual interest rate, compounded monthly",
        "min": 0
      },
      {
        "name": "months",
        "type": "integer",
        "required": true,
        "description": "Number of monthly payments (loan term in months)",
        "min": 1
      }
    ],
    "outputs": [
      {
        "name": "monthly_payment",
        "unit": "currency units",
        "description": "Fixed payment due each month"
      }
    ],
    "steps": [
      "Convert the annual rate to a decimal: r = annual_rate_percent / 100.",
      "Monthly rate i = r / 12.",
      "If i = 0, monthly_payment = principal / months.",
      "Otherwise, monthly_payment = principal * i * (1 + i)^months / ((1 + i)^months - 1) (the standard annuity payment formula).",
      "Round monthly_payment to 2 decimals (money to cents)."
    ],
    "constants": [],
    "examples": [
      {
        "name": "worked example",
        "inputs": {
          "principal": 200000,
          "annual_rate_percent": 6,
          "months": 360
        },
        "expected": {
          "answer": "$1,199.10"
        },
        "check": "hand computation: i = 0.005, factor = 1.005^360 = 6.022575..., payment = 200000*0.005*6.022575/(6.022575-1) = 1199.10"
      },
      {
        "name": "test vector: zero interest",
        "inputs": {
          "principal": 12000,
          "annual_rate_percent": 0,
          "months": 12
        },
        "expected": {
          "answer": "$1,000.00"
        },
        "check": "hand computation: zero-rate branch, payment = 12000/12 = 1000.00"
      }
    ],
    "disclaimer": null,
    "deck_category": "finance"
  },
  "status": "minted",
  "kind": "method",
  "provenanceClass": "own_question",
  "provenance": {
    "schema": "card_provenance/2.0.0",
    "chain": [
      {
        "source": {
          "kind": "edition_page",
          "value": "Brealey, Myers, Allen, Principles of Corporate Finance, 13th ed., Chapter 3, section 3-3 (Loan Amortization)",
          "retrieved_utc": "2026-09-30T19:31:29Z"
        },
        "sha256": "a810011267685d9ab859ae100fe6fc1aaba2bbf5e703e8e590f747e2e9b7a162",
        "supersedes": null,
        "added_utc": "2026-09-30T22:39:30.722Z",
        "added_by": "method:Amortized loan payment",
        "why": "the method that computed this answer",
        "check": null,
        "status_label": "pending",
        "signature": null
      }
    ]
  }
}