module.exports = {
  slug: "rule-of-72-and-exact-doubling-time",
  title: "Rule of 72 and exact doubling time",
  deck_category: "finance",
  description: "Estimates the years to double an investment with the Rule of 72 approximation and computes the exact doubling time with logarithms.",
  inputs: [
    { name: "annual_rate_percent", type: "number", unit: "%", required: true, description: "Annual compound growth rate", min: 0.0001 }
  ],
  outputs: [
    { name: "approx_years", unit: "years", description: "Rule of 72 approximation: 72 / rate" },
    { name: "exact_years", unit: "years", description: "Exact doubling time using logarithms" }
  ],
  steps: [
    "Rule of 72 approximation: approx_years = 72 / annual_rate_percent.",
    "Convert the rate to a decimal: r = annual_rate_percent / 100.",
    "Exact doubling time: exact_years = ln(2) / ln(1 + r).",
    "Round approx_years and exact_years to 2 decimals."
  ],
  constants: [
    { name: "rule_of_72_numerator", value: 72, unit: "dimensionless", source: 0 }
  ],
  sources: [
    { kind: "edition_page", value: "Brealey, Myers, Allen, Principles of Corporate Finance, 13th ed., Chapter 3, box on the Rule of 72", title: "Principles of Corporate Finance", publisher: "McGraw-Hill", retrieved_utc: "2026-09-30T19:31:29Z", note: "Rule of 72 approximation and the exact doubling-time formula t = ln(2)/ln(1+r)" }
  ],
  disclaimer: null,
  questionText(inputs) {
    return `Using the Rule of 72 and the exact logarithmic formula, how many years does it take to double an investment growing at ${inputs.annual_rate_percent}% per year?`;
  },
  run(inputs) {
    const { annual_rate_percent } = inputs;
    if (typeof annual_rate_percent !== "number" || annual_rate_percent <= 0) throw new Error("annual_rate_percent must be a positive number");
    const approx_years = Math.round((72 / annual_rate_percent) * 100) / 100;
    const r = annual_rate_percent / 100;
    const exact_years = Math.round((Math.log(2) / Math.log(1 + r)) * 100) / 100;
    return {
      answer: `Approximately ${approx_years.toFixed(2)} years (Rule of 72); exactly ${exact_years.toFixed(2)} years`,
      values: { approx_years, exact_years }
    };
  },
  examples: [
    {
      name: "worked example",
      inputs: { annual_rate_percent: 8 },
      expected: { answer: "Approximately 9.00 years (Rule of 72); exactly 9.01 years" },
      check: "hand computation: approx = 72/8 = 9.00; exact = ln(2)/ln(1.08) = 0.693147.../0.076961... = 9.0065..., rounds to 9.01"
    },
    {
      name: "test vector: low rate",
      inputs: { annual_rate_percent: 3 },
      expected: { answer: "Approximately 24.00 years (Rule of 72); exactly 23.45 years" },
      check: "hand computation: approx = 72/3 = 24.00; exact = ln(2)/ln(1.03) = 0.693147.../0.029559... = 23.4498..., rounds to 23.45"
    }
  ]
};