{
  "address": "8a524043e544c574b2a72e729fe3d80d",
  "category": "other",
  "question": "For a $200000 loan at 6% annual interest amortized over 360 months, how much of payment number 1 is interest, how much is principal, and what is the remaining balance after it?",
  "answer": "Interest $1,000.00, principal $199.10, remaining balance $199,800.90",
  "askedBy": {
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  "answeredBy": "method",
  "madeAt": "2026-09-30T22:39:30.722Z",
  "validUntil": null,
  "validityClass": "forever",
  "sources": [
    {
      "label": "Principles of Corporate Finance",
      "url": null
    }
  ],
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  "supersededBy": null,
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  "answerMethod": "method",
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  "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": "381ba314c755b95318045a4f1cfb15de3cfa2bb6bc32613452873bd0c9644602",
  "runOne": null,
  "cardContractVersion": "card_contract/1",
  "deck_id": "method-deck",
  "deck_title": "Method Deck",
  "method": {
    "name": "Amortization schedule row",
    "version": "1",
    "source_url_or_file": "methods/amortization-schedule-row.cjs",
    "sha256_of_method_file": "d7611c37d0df74df61327a266c3593af0c1c17811b0bc4366e3731d3b6394b38"
  },
  "receipt": {
    "inSubstrate": false,
    "local": true,
    "modelCallsAtMint": 0,
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  "method_deck": {
    "inputs": [
      {
        "name": "principal",
        "type": "number",
        "unit": "currency units",
        "required": true,
        "description": "Original loan amount",
        "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": "Total number of monthly payments in the loan",
        "min": 1
      },
      {
        "name": "payment_number",
        "type": "integer",
        "required": true,
        "description": "Which payment to report (1 = first payment)",
        "min": 1
      }
    ],
    "outputs": [
      {
        "name": "interest_portion",
        "unit": "currency units",
        "description": "Interest paid in this payment"
      },
      {
        "name": "principal_portion",
        "unit": "currency units",
        "description": "Principal paid in this payment"
      },
      {
        "name": "remaining_balance",
        "unit": "currency units",
        "description": "Balance remaining after this payment"
      }
    ],
    "steps": [
      "Convert the annual rate to a decimal: r = annual_rate_percent / 100; monthly rate i = r / 12.",
      "Compute the fixed monthly payment using the standard annuity formula: payment = principal * i * (1+i)^months / ((1+i)^months - 1) (or principal/months if i = 0).",
      "Starting from balance = principal, iterate payment by payment: interest_this = balance * i; principal_this = payment - interest_this; balance = balance - principal_this.",
      "Stop at payment_number and report that payment's interest_portion, principal_portion, and the resulting remaining_balance.",
      "Round every reported amount to 2 decimals (money to cents); the final row's remaining_balance is clamped to 0 if within half a cent."
    ],
    "constants": [],
    "examples": [
      {
        "name": "worked example",
        "inputs": {
          "principal": 200000,
          "annual_rate_percent": 6,
          "months": 360,
          "payment_number": 1
        },
        "expected": {
          "answer": "Interest $1,000.00, principal $199.10, remaining balance $199,800.90"
        },
        "check": "hand computation: payment = 1199.10 (see loan-payment-amortized), first month interest = 200000*0.005 = 1000.00, principal = 1199.10-1000.00 = 199.10, balance = 200000-199.10 = 199800.90"
      },
      {
        "name": "test vector: last payment fully retires balance",
        "inputs": {
          "principal": 12000,
          "annual_rate_percent": 0,
          "months": 12,
          "payment_number": 12
        },
        "expected": {
          "answer": "Interest $0.00, principal $1,000.00, remaining balance $0.00"
        },
        "check": "hand computation: zero interest loan, each payment is 1000.00 principal, after 12 payments balance is exactly 0"
      }
    ],
    "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": "4cfa8954300537acb5d732dc936a39d21dd0acd595d998298e6cc89a2b89521b",
        "supersedes": null,
        "added_utc": "2026-09-30T22:39:30.722Z",
        "added_by": "method:Amortization schedule row",
        "why": "the method that computed this answer",
        "check": null,
        "status_label": "pending",
        "signature": null
      }
    ]
  }
}