{
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  "question": "What is the percent change and the compound annual growth rate (CAGR) for a value that went from $1000 to $2000 over 5 years?",
  "answer": "Percent change 100.00%, CAGR 14.87%",
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  "sources": [
    {
      "label": "Principles of Corporate Finance",
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    }
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    "kind": "edition_page",
    "value": "Brealey, Myers, Allen, Principles of Corporate Finance, 13th ed., Chapter 3, discussion of compound growth rates",
    "retrieved_utc": "2026-09-30T19:31:29Z"
  },
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  "method": {
    "name": "Percent change and CAGR",
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  "method_deck": {
    "inputs": [
      {
        "name": "start_value",
        "type": "number",
        "unit": "currency units",
        "required": true,
        "description": "Starting value",
        "min": 0.0001
      },
      {
        "name": "end_value",
        "type": "number",
        "unit": "currency units",
        "required": true,
        "description": "Ending value",
        "min": 0
      },
      {
        "name": "years",
        "type": "number",
        "unit": "years",
        "required": true,
        "description": "Number of years between start and end",
        "min": 0.0001
      }
    ],
    "outputs": [
      {
        "name": "percent_change",
        "unit": "%",
        "description": "Simple percent change from start_value to end_value"
      },
      {
        "name": "cagr_percent",
        "unit": "%",
        "description": "Compound annual growth rate"
      }
    ],
    "steps": [
      "percent_change = (end_value - start_value) / start_value * 100.",
      "CAGR as a decimal = (end_value / start_value) ^ (1 / years) - 1.",
      "cagr_percent = CAGR decimal * 100.",
      "Round percent_change and cagr_percent to 2 decimals."
    ],
    "constants": [],
    "examples": [
      {
        "name": "worked example",
        "inputs": {
          "start_value": 1000,
          "end_value": 2000,
          "years": 5
        },
        "expected": {
          "answer": "Percent change 100.00%, CAGR 14.87%"
        },
        "check": "hand computation: percent_change = (2000-1000)/1000*100 = 100.00; CAGR = (2)^(1/5)-1 = 0.148698..., 14.8698% rounds to 14.87%"
      },
      {
        "name": "test vector: decline",
        "inputs": {
          "start_value": 5000,
          "end_value": 4000,
          "years": 2
        },
        "expected": {
          "answer": "Percent change -20.00%, CAGR -10.56%"
        },
        "check": "hand computation: percent_change = (4000-5000)/5000*100 = -20.00; CAGR = (4000/5000)^(1/2)-1 = 0.8^0.5-1 = 0.894427-1 = -0.105573, -10.5573% rounds to -10.56%"
      }
    ],
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}