{"slug":"the-rule-of-72","qid":"doubling_gap","label":"Years to double: the Rule of 72 on the average against the compounded path","post_title":"The Rule of 72 (and Where It Breaks)","post_url":"/blog/the-rule-of-72#q-doubling_gap","columns":["ticker","rule_of_72_years","compounded_years","extra_years","extra_time_pct"],"rows":[{"ticker":"ARKK","rule_of_72_years":4.08,"compounded_years":6.66,"extra_years":2.58,"extra_time_pct":63.3},{"ticker":"SPY","rule_of_72_years":5.96,"compounded_years":6.6,"extra_years":0.64,"extra_time_pct":10.7},{"ticker":"AMD","rule_of_72_years":1.31,"compounded_years":1.82,"extra_years":0.51,"extra_time_pct":38.8},{"ticker":"QQQ","rule_of_72_years":3.9,"compounded_years":4.32,"extra_years":0.41,"extra_time_pct":10.6},{"ticker":"MSFT","rule_of_72_years":2.8,"compounded_years":3.15,"extra_years":0.35,"extra_time_pct":12.4}],"shape":"table","sql":"WITH daily AS\n(\n    SELECT\n        ticker,\n        date,\n        toFloat64(max(close)) AS close_px\n    FROM global_markets.stocks_daily_aggs\n    WHERE ticker IN ('SPY', 'QQQ', 'MSFT', 'ARKK', 'AMD')\n      AND date >= '2015-01-02'\n      AND date <= '2024-12-31'\n      AND close > 0\n    GROUP BY ticker, date\n),\nrets AS\n(\n    SELECT\n        ticker,\n        close_px / nullIf(lagInFrame(close_px) OVER (PARTITION BY ticker ORDER BY date ASC), 0) - 1 AS r\n    FROM daily\n),\nstats AS\n(\n    SELECT\n        ticker,\n        avg(r) * 252          AS arith_annual,\n        avg(log(1 + r)) * 252 AS log_annual\n    FROM rets\n    WHERE r IS NOT NULL\n      AND isFinite(r)\n    GROUP BY ticker\n)\nSELECT\n    ticker,\n    round(72.0 / (arith_annual * 100), 2)                                       AS rule_of_72_years,\n    round(log(2) / log_annual, 2)                                               AS compounded_years,\n    round(log(2) / log_annual - 72.0 / (arith_annual * 100), 2)                 AS extra_years,\n    round((log(2) / log_annual) / (72.0 / (arith_annual * 100)) * 100 - 100, 1) AS extra_time_pct\nFROM stats\nORDER BY extra_years DESC","computed_at":"2026-10-09T15:39:34.153984+00:00","elapsed":0.004121409}