module.exports = {
  slug: "loan-payment-amortized",
  title: "Amortized loan payment",
  deck_category: "finance",
  description: "Computes the fixed monthly payment for a fully amortizing loan using the standard annuity payment formula.",
  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: [],
  sources: [
    { kind: "edition_page", value: "Brealey, Myers, Allen, Principles of Corporate Finance, 13th ed., Chapter 3, section 3-3 (Loan Amortization)", title: "Principles of Corporate Finance", publisher: "McGraw-Hill", retrieved_utc: "2026-09-30T19:31:29Z", note: "Standard fixed-payment annuity formula for amortizing loans" }
  ],
  disclaimer: null,
  questionText(inputs) {
    return `What is the fixed monthly payment on a $${inputs.principal} loan at ${inputs.annual_rate_percent}% annual interest amortized over ${inputs.months} months?`;
  },
  run(inputs) {
    const { principal, annual_rate_percent, months } = inputs;
    if (typeof principal !== "number" || principal < 0) throw new Error("principal must be a non-negative number");
    if (typeof annual_rate_percent !== "number" || annual_rate_percent < 0) throw new Error("annual_rate_percent must be a non-negative number");
    if (!Number.isInteger(months) || months <= 0) throw new Error("months must be a positive integer");
    const r = annual_rate_percent / 100;
    const i = r / 12;
    let monthly_payment;
    if (i === 0) {
      monthly_payment = principal / months;
    } else {
      const factor = Math.pow(1 + i, months);
      monthly_payment = (principal * i * factor) / (factor - 1);
    }
    monthly_payment = Math.round(monthly_payment * 100) / 100;
    return {
      answer: `$${monthly_payment.toFixed(2).replace(/\B(?=(\d{3})+(?!\d))/g, ",")}`,
      values: { monthly_payment }
    };
  },
  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"
    }
  ]
};