{"slug":"the-rule-of-72","qid":"rule_vs_exact","label":"Rule of 72 against the exact doubling time, by annual return","post_title":"The Rule of 72 (and Where It Breaks)","post_url":"/blog/the-rule-of-72#q-rule_vs_exact","columns":["annual_return","rule_of_72_years","exact_years","gap_years"],"rows":[{"annual_return":"1%","rule_of_72_years":72,"exact_years":69.66,"gap_years":2.34},{"annual_return":"2%","rule_of_72_years":36,"exact_years":35,"gap_years":1},{"annual_return":"3%","rule_of_72_years":24,"exact_years":23.45,"gap_years":0.55},{"annual_return":"4%","rule_of_72_years":18,"exact_years":17.67,"gap_years":0.33},{"annual_return":"6%","rule_of_72_years":12,"exact_years":11.9,"gap_years":0.1},{"annual_return":"8%","rule_of_72_years":9,"exact_years":9.01,"gap_years":0.01},{"annual_return":"10%","rule_of_72_years":7.2,"exact_years":7.27,"gap_years":0.07},{"annual_return":"12%","rule_of_72_years":6,"exact_years":6.12,"gap_years":0.12},{"annual_return":"15%","rule_of_72_years":4.8,"exact_years":4.96,"gap_years":0.16},{"annual_return":"20%","rule_of_72_years":3.6,"exact_years":3.8,"gap_years":0.2},{"annual_return":"25%","rule_of_72_years":2.88,"exact_years":3.11,"gap_years":0.23}],"shape":"ranking","sql":"SELECT\n    concat(toString(annual_pct), '%')        AS annual_return,\n    round(72.0 / annual_pct, 2)              AS rule_of_72_years,\n    round(exact, 2)                          AS exact_years,\n    round(abs(72.0 / annual_pct - exact), 2) AS gap_years\nFROM\n(\n    SELECT\n        annual_pct,\n        log(2) / log(1 + annual_pct / 100.0) AS exact\n    FROM\n    (\n        SELECT arrayJoin([1, 2, 3, 4, 6, 8, 10, 12, 15, 20, 25]) AS annual_pct\n    )\n)\nORDER BY annual_pct ASC","computed_at":"2026-10-09T15:39:33.876098+00:00","elapsed":0.009517707}