{"slug":"the-rule-of-72","qid":"vol_doubling_curve","label":"An 8% average return at rising volatility: compound rate and doubling time","post_title":"The Rule of 72 (and Where It Breaks)","post_url":"/blog/the-rule-of-72#q-vol_doubling_curve","columns":["annual_volatility","compound_return_pct","doubling_years"],"rows":[{"annual_volatility":"0%","compound_return_pct":8,"doubling_years":9},{"annual_volatility":"5%","compound_return_pct":7.88,"doubling_years":9.1},{"annual_volatility":"10%","compound_return_pct":7.5,"doubling_years":9.6},{"annual_volatility":"15%","compound_return_pct":6.88,"doubling_years":10.4},{"annual_volatility":"20%","compound_return_pct":6,"doubling_years":11.9},{"annual_volatility":"25%","compound_return_pct":4.88,"doubling_years":14.6},{"annual_volatility":"30%","compound_return_pct":3.5,"doubling_years":20.1},{"annual_volatility":"35%","compound_return_pct":1.88,"doubling_years":37.3}],"shape":"ranking","sql":"SELECT\n    concat(toString(vol_pct), '%')       AS annual_volatility,\n    round(compound * 100, 2)             AS compound_return_pct,\n    round(log(2) / log(1 + compound), 1) AS doubling_years\nFROM\n(\n    SELECT\n        vol_pct,\n        0.08 - 0.5 * pow(vol_pct / 100.0, 2) AS compound\n    FROM\n    (\n        SELECT arrayJoin([0, 5, 10, 15, 20, 25, 30, 35]) AS vol_pct\n    )\n)\nORDER BY vol_pct ASC","computed_at":"2026-10-09T15:39:33.968159+00:00","elapsed":0.004309713}