{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"rule-of-72"},"result":{"entity_type":"calculator","id":"rule-of-72","calculator_id":"rule-of-72","canonical_url":"https://tttkmbb.com/finance/rule-of-72","name":"Rule of 72 Calculator","title":"Rule of 72 Calculator – Years to Double an Investment at a Given Rate","category":"finance","category_name":"Finance","tool_name":"calculate_rule_of_72","featured_mcp_tool":false,"description":"Estimates the doubling time of an amount growing at a fixed annual rate with the Rule of 72, and compares it with the exact result ln 2 / ln(1 + r) for annual compounding and ln 2 / r for continuous compounding.","use_when":"You want a quick mental-math estimate of how long money (or debt, or prices) takes to double at a given annual growth rate, plus the exact figure.","do_not_use_when":"You need the balance after a specific number of years (use compound-interest) or the rate implied by two values (use cagr).","inputs":[{"name":"annual_rate_percent","label":"Annual growth rate","type":"number","unit":"%","required":true,"max":100,"exclusive_min":0,"description":"Annual interest, return or inflation rate in percent; 8 means 8 %.","example":8}],"outputs":[{"name":"rule_of_72_years","label":"Doubling time (Rule of 72)","type":"number","unit":"years","decimals":2,"description":"72 / annual_rate_percent."},{"name":"exact_years","label":"Doubling time (exact, annual compounding)","type":"number","unit":"years","decimals":2,"description":"ln(2) / ln(1 + rate)."},{"name":"continuous_years","label":"Doubling time (continuous compounding)","type":"number","unit":"years","decimals":2,"description":"ln(2) / rate ≈ 69.3 / annual_rate_percent."},{"name":"rule_error_percent","label":"Rule of 72 error","type":"number","unit":"%","decimals":2,"description":"(rule_of_72_years − exact_years) / exact_years × 100."},{"name":"years_to_triple_exact","label":"Tripling time (exact)","type":"number","unit":"years","decimals":2,"description":"ln(3) / ln(1 + rate)."}],"input_schema":{"type":"object","properties":{"annual_rate_percent":{"description":"Annual interest, return or inflation rate in percent; 8 means 8 %. Unit: %.","type":"number","maximum":100,"exclusiveMinimum":0,"examples":[8],"x-unit":"%"}},"additionalProperties":false,"required":["annual_rate_percent"]},"output_schema":{"type":"object","properties":{"rule_of_72_years":{"description":"72 / annual_rate_percent. Unit: years.","type":"number","x-unit":"years"},"exact_years":{"description":"ln(2) / ln(1 + rate). Unit: years.","type":"number","x-unit":"years"},"continuous_years":{"description":"ln(2) / rate ≈ 69.3 / annual_rate_percent. Unit: years.","type":"number","x-unit":"years"},"rule_error_percent":{"description":"(rule_of_72_years − exact_years) / exact_years × 100. Unit: %.","type":"number","x-unit":"%"},"years_to_triple_exact":{"description":"ln(3) / ln(1 + rate). Unit: years.","type":"number","x-unit":"years"}}},"formula":"rule_of_72_years = 72 / annual_rate_percent; exact_years = ln(2) / ln(1 + annual_rate_percent/100); continuous_years = ln(2) / (annual_rate_percent/100)","method":"The rule is a first-order approximation that is most accurate between about 6 % and 10 %; below that the Rule of 70 or 69.3 is closer, and at high rates the rule overstates the doubling time.","sources":[{"name":"Wikipedia – Rule of 72","url":"https://en.wikipedia.org/wiki/Rule_of_72","type":"reference","retrieved_at":"2026-09-23"},{"name":"Investopedia – The Rule of 72: Definition, Usefulness and How to Use It","url":"https://www.investopedia.com/terms/r/ruleof72.asp","type":"reference","retrieved_at":"2026-09-23"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"8 % per year","inputs":{"annual_rate_percent":8},"expected":{"rule_of_72_years":9,"exact_years":9.01,"continuous_years":8.66,"rule_error_percent":-0.07},"url":"https://tttkmbb.com/api/v1/calculate/rule-of-72?annual_rate_percent=8"},{"name":"6 % per year","inputs":{"annual_rate_percent":6},"expected":{"rule_of_72_years":12,"exact_years":11.9,"continuous_years":11.55,"years_to_triple_exact":18.85},"url":"https://tttkmbb.com/api/v1/calculate/rule-of-72?annual_rate_percent=6"}],"faq":[{"q":"Why 72 and not 69.3?","a":"ln 2 ≈ 0.693 gives the exact continuous-compounding rule, but 72 has many divisors (2, 3, 4, 6, 8, 9, 12) and happens to correct for annual compounding near 8 %."},{"q":"Does it work for inflation or debt?","a":"Yes, any constant growth rate: at 3 % inflation prices double in about 24 years; at 18 % APR an unpaid credit-card balance doubles in about 4 years."}],"tags":["rule of 72","doubling time","how long to double money","rule of 70","compound growth"],"related":[{"calculator_id":"compound-interest","reason":"Exact balance after any number of years."},{"calculator_id":"cagr","reason":"Growth rate implied by a starting and ending value."}],"links":{"html":"https://tttkmbb.com/finance/rule-of-72","markdown":"https://tttkmbb.com/finance/rule-of-72.md","json":"https://tttkmbb.com/finance/rule-of-72.json","api":"https://tttkmbb.com/api/v1/calculate/rule-of-72","schema":"https://tttkmbb.com/api/v1/calculators/rule-of-72","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:32:53Z"}