{"format":"alysly-page/1","url":"https://alysly.com/learn/rule-of-72/","json":"https://alysly.com/json/learn/rule-of-72/index.json","lang":"en-US","title":"The Rule of 72: Estimating Doubling Time – Alysly","description":"A rule of thumb for compounding: 72 divided by the annual return gives roughly the years until a sum doubles – with its limits and the exact calculation.","published":"2026-07-13T11:24:42+02:00","modified":"2026-11-01T18:26:04+01:00","alternates":[{"lang":"de-DE","url":"https://alysly.com/de/lernen/72er-regel/","json":"https://alysly.com/json/de/lernen/72er-regel/index.json"}],"about":"Machine-readable version of the page at url. It contains the text, tables and key figures published there, but not the interactive charts and tools.","breadcrumb":[{"name":"Investing & Trading Basics","url":"https://alysly.com/learn/"},{"name":"Level 0","url":"https://alysly.com/learn/#level-0"},{"name":"The Rule of 72: Estimating Doubling Time","url":"https://alysly.com/learn/rule-of-72/"}],"content":[{"type":"paragraph","text":"Level 0 Investing & ETF Basics · Part 8/16"},{"type":"heading","level":1,"text":"The Rule of 72: Estimating Doubling Time"},{"type":"paragraph","text":"By Alexander Bock, founder and data analyst","links":[{"text":"Alexander Bock","href":"https://alysly.com/about/"}]},{"type":"paragraph","text":"The Rule of 72 is an approximation: 72 divided by the annual return in percent gives roughly the years until a sum doubles."},{"type":"image","src":"https://alysly.com/img/ta/rule-72.54b02388c8fa29388f5913346396caf05e184b4fe4b7488dfb55098e3f346455.webp","alt":"Bar pairs for returns of 2 to 12 percent: doubling time by the rule of 72 and calculated exactly"},{"type":"paragraph","text":"Years to double at 2, 4, 6, 8, 10 and 12% return: gray by the rule of 72 (72 ÷ return), green calculated exactly. Between roughly 6 and 10%, the rule is almost exact; at 2% it overstates the time by nearly a year."},{"type":"list","ordered":false,"items":["6% → 72 / 6 = 12 years","8% → 72 / 8 = 9 years","4% → 72 / 4 = 18 years"]},{"type":"paragraph","text":"The rule assumes a constant return, which markets never deliver. It does show how strongly a few percentage points of return or cost, and the length of the holding period, change the outcome over decades."},{"type":"paragraph","text":"The savings-plan calculator gives the exact figure; the fee article shows how ongoing costs stretch the doubling time.","links":[{"text":"savings-plan calculator","href":"https://alysly.com/tools/savings-plan/"},{"text":"fee article","href":"https://alysly.com/learn/etf-fees/"}]},{"type":"heading","level":2,"id":"where-the-72-comes-from","text":"Where the 72 Comes From"},{"type":"paragraph","text":"To be exact, a sum doubles in ln 2 ÷ ln(1 + r) years, where r is the annual return as a decimal. For small returns, ln(1 + r) is roughly r, which gives 69.3 ÷ the return in percent. The 72 sits a little above that because it fits typical returns of 6% to 10% more closely. It also divides evenly by many numbers: 2, 3, 4, 6, 8, 9 and 12."},{"type":"heading","level":2,"id":"how-accurate-the-rule-is","text":"How Accurate the Rule Is"},{"type":"table","caption":"The Rule of 72: Estimating Doubling Time","columns":["Return","72 ÷ return","exact"],"rows":[["2%","36.0 years","35.0 years"],["4%","18.0 years","17.7 years"],["6%","12.0 years","11.9 years"],["8%","9.0 years","9.0 years"],["10%","7.2 years","7.3 years"],["15%","4.8 years","5.0 years"],["20%","3.6 years","3.8 years"]]},{"type":"paragraph","text":"Between 4% and 12%, the rule is off by less than half a year. At very low returns it overstates the time, at high returns it understates it."},{"type":"heading","level":2,"id":"inflation-and-costs","text":"Inflation and Costs"},{"type":"paragraph","text":"The same arithmetic works for anything that grows at a fixed rate each year. At 2% inflation, purchasing power halves after 72 ÷ 2 = 36 years, exactly after 35. Costs translate the same way. If a fund earns 7% before costs, money doubles in about 10.5 years with 0.2% in ongoing costs (6.8% net). With 1.5% (5.5% net), it takes almost 13 years."},{"type":"heading","level":2,"id":"limits","text":"Limits"},{"type":"list","ordered":false,"items":["The rule assumes a constant return. Swings slow growth down: a year at −20% followed by one at +20% does not add up to zero but to −4%.","It applies to a single lump sum, not to regular contributions.","Taxes stretch the doubling time further."]},{"type":"paragraph","text":"Information only, not investment advice."},{"type":"list","ordered":false,"items":[{"text":"Previous Savings Plan or Lump Sum: What Historical Data Shows","href":"https://alysly.com/learn/savings-plan-vs-lump-sum/"},{"text":"Next ETFs & Tax in Germany: The Essentials","href":"https://alysly.com/learn/etf-taxes-germany/"}]},{"type":"heading","level":2,"text":"Indices"},{"type":"table","caption":"Indices, performance over the selected period","columns":["Index","1M"],"rows":[[{"text":"Dow Jones","href":"https://alysly.com/markets/indices/dow-jones/"},{"text":"+1.7%","data":{"m1":"+1.7%","m3":"-1.4%","m6":"+4.5%","ytd":"+7.6%","max":"+30.1%"}}],[{"text":"S&P 500","href":"https://alysly.com/markets/indices/sp500/"},{"text":"-0.9%","data":{"m1":"-0.9%","m3":"+1.2%","m6":"+4.9%","ytd":"+10.8%","max":"+35.8%"}}],[{"text":"MSCI World","href":"https://alysly.com/markets/indices/msci-world/"},{"text":"-0.8%","data":{"m1":"-0.8%","m3":"+0.6%","m6":"+4.0%","ytd":"+10.2%","max":"+35.3%"}}],[{"text":"MSCI ACWI","href":"https://alysly.com/markets/indices/msci-acwi/"},{"text":"-1.7%","data":{"m1":"-1.7%","m3":"-0.2%","m6":"+2.9%","ytd":"+10.3%","max":"+41.7%"}}]]},{"type":"heading","level":2,"text":"ETFs"},{"type":"table","caption":"ETFs, performance over the selected period","columns":["Fund","1M"],"rows":[[{"text":"SPDR S&P 500 ETF Trust SPY","links":[{"text":"SPDR S&P 500 ETF Trust","href":"https://alysly.com/markets/etfs/us/spy/"}]},{"text":"-0.9%","data":{"m1":"-0.9%","m3":"+1.2%","m6":"+4.9%","ytd":"+10.8%","max":"+35.8%"}}],[{"text":"Vanguard S&P 500 ETF VOO","links":[{"text":"Vanguard S&P 500 ETF","href":"https://alysly.com/markets/etfs/us/voo/"}]},{"text":"-0.9%","data":{"m1":"-0.9%","m3":"+1.2%","m6":"+4.9%","ytd":"+10.8%","max":"+34.3%"}}],[{"text":"iShares Core MSCI World UCITS ETF USD (Acc) EUNL","links":[{"text":"iShares Core MSCI World UCITS ETF USD (Acc)","href":"https://alysly.com/markets/etfs/ishares-core-msci-world-ucits-etf-usd-acc/"}]},{"text":"-0.8%","data":{"m1":"-0.8%","m3":"+0.6%","m6":"+4.6%","ytd":"+10.9%","max":"+489.0%"}}],[{"text":"Xtrackers MSCI Emerging Markets UCITS ETF 1c XMME","links":[{"text":"Xtrackers MSCI Emerging Markets UCITS ETF 1c","href":"https://alysly.com/markets/etfs/xtrackers-msci-emerging-markets-ucits-etf-1c/"}]},{"text":"-6.3%","data":{"m1":"-6.3%","m3":"+2.4%","m6":"+0.7%","ytd":"+15.2%","max":"+95.2%"}}]]},{"type":"heading","level":2,"text":"Stocks"},{"type":"table","caption":"Stocks, performance over the selected period","columns":["Stock","1M"],"rows":[[{"text":"NVIDIA Corporation NVDA","links":[{"text":"NVIDIA Corporation","href":"https://alysly.com/markets/stocks/nvidia-corporation/"},{"text":"United States","href":"https://alysly.com/markets/stocks/browse/?country=United%20States"}]},{"text":"-10.4%","data":{"m1":"-10.4%","m3":"+1.9%","m6":"+3.1%","ytd":"+9.7%","max":"+60.6%"}}],[{"text":"Apple Inc. AAPL","links":[{"text":"Apple Inc.","href":"https://alysly.com/markets/stocks/apple-inc/"},{"text":"United States","href":"https://alysly.com/markets/stocks/browse/?country=United%20States"}]},{"text":"+3.5%","data":{"m1":"+3.5%","m3":"+11.6%","m6":"+23.0%","ytd":"+26.8%","max":"+51.4%"}}],[{"text":"Tesla Inc. TSLA","links":[{"text":"Tesla Inc.","href":"https://alysly.com/markets/stocks/tesla-inc/"},{"text":"United States","href":"https://alysly.com/markets/stocks/browse/?country=United%20States"}]},{"text":"+12.7%","data":{"m1":"+12.7%","m3":"+28.5%","m6":"+2.3%","ytd":"-11.1%","max":"+65.9%"}}]]},{"type":"paragraph","text":"Data note 1","href":"#dn-1"},{"type":"heading","level":2,"text":"More Studies"},{"type":"list","ordered":false,"items":[{"text":"Jul 21, 2026 Collectibles ×5.4 for the same cards, matched-model index, Mar 2022 – Aug 2026 Is the Pokémon Card Market in a Bubble? 4,159 Sales Analyzed Prices for PSA-graded cards multiplied. Measured on the same cards they rose 438%, while the raw median shows 786% because pricier cards came up for sale later.","href":"https://alysly.com/analysis/pokemon-card-market-bubble/"},{"text":"May 19, 2026 Crypto 45.6% Bitcoin’s annualized volatility, Jul 2024 – Sep 2026 Bitcoin in Investment Portfolios: The Real Numbers Bitcoin is calmer than it was and still about three times as volatile as the stock market. It moves with stocks, not with gold.","href":"https://alysly.com/analysis/bitcoin-investment-portfolios/"},{"text":"Mar 17, 2026 Wealth €1.2m needed for €3,000 a month indefinitely at a 3% real return Living Off Your Returns: What It Really Takes The capital you need is arithmetic. The return you assume is a guess, and it can triple the answer.","href":"https://alysly.com/analysis/living-off-returns/"}]},{"type":"paragraph","text":"View all studies","href":"https://alysly.com/analysis/#studies"},{"type":"heading","level":2,"text":"Learn"},{"type":"list","ordered":false,"items":[{"text":"ETFs & Tax in Germany: The Essentials Teilfreistellung, Vorabpauschale and the saver's allowance: how ETFs are taxed in Germany, explained clearly.","href":"https://alysly.com/learn/etf-taxes-germany/"},{"text":"MSCI World Criticism: How Big Is the US Concentration? The MSCI World is criticized for its heavy US weighting. The current breakdown by country and sector, and which fund types change the weighting.","href":"https://alysly.com/learn/msci-world-criticism/"}]},{"type":"paragraph","text":"Course overview","href":"https://alysly.com/learn/"},{"type":"paragraph","text":"Updated Nov 1, 2026 · Content and figures checked Nov 1, 2026"},{"type":"heading","level":2,"id":"note-legend-h","text":"Data Notes"},{"type":"paragraph","text":"All calculations run automatically and are not investment advice."},{"type":"list","ordered":true,"items":[{"id":"dn-1","text":"Returns computed automatically from the price series, excluding dividends, taxes and costs."}]},{"type":"paragraph","text":"Data and methodology: Alysly · Responsible for content: Alexander Bock","links":[{"text":"Alysly","href":"https://alysly.com/methodology/"},{"text":"Alexander Bock","href":"https://alysly.com/about/"}]},{"type":"paragraph","text":"View all data notes","href":"https://alysly.com/notes/"}],"structured_data":[{"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://alysly.com/#org","name":"Alysly","url":"https://alysly.com/","logo":{"@type":"ImageObject","url":"https://alysly.com/img/icon-512.png","width":512,"height":512},"description":"Data-driven insights, transparent analysis and powerful tools for long-term investors.","email":"mail@alysly.com","contactPoint":{"@type":"ContactPoint","contactType":"customer support","email":"mail@alysly.com","availableLanguage":["de","en"]},"address":{"@type":"PostalAddress","addressLocality":"Haltern am See","postalCode":"45721","addressCountry":"DE"},"founder":{"@id":"https://alysly.com/#founder"},"sameAs":["https://www.linkedin.com/company/alyslycom/","https://www.youtube.com/@alyslycom","https://x.com/alyslycom"],"publishingPrinciples":"https://alysly.com/methodology/"},{"@type":"Person","@id":"https://alysly.com/#founder","name":"Alexander Bock","jobTitle":"Founder and data analyst","url":"https://alysly.com/about/","sameAs":["https://www.linkedin.com/in/abxk/"]},{"@type":"WebSite","@id":"https://alysly.com/#site","url":"https://alysly.com/","name":"Alysly","alternateName":"Alysly Investment Analysis","inLanguage":"en-US","publisher":{"@id":"https://alysly.com/#org"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://alysly.com/markets/stocks/browse/?q={search_term_string}"},"query-input":"required name=search_term_string"}},{"@type":"WebPage","@id":"https://alysly.com/learn/rule-of-72/#webpage","url":"https://alysly.com/learn/rule-of-72/","name":"The Rule of 72: Estimating Doubling Time – Alysly","description":"A rule of thumb for compounding: 72 divided by the annual return gives roughly the years until a sum doubles – with its limits and the exact calculation.","inLanguage":"en-US","isPartOf":{"@id":"https://alysly.com/#site"},"dateModified":"2026-11-01T18:26:04+01:00","publisher":{"@id":"https://alysly.com/#org"},"mainEntity":{"@id":"https://alysly.com/learn/rule-of-72/#entity"},"primaryImageOfPage":{"@type":"ImageObject","url":"https://alysly.com/img/ta/rule-72-og.8b5d1ec892f31d3e7e2a53857c9c680766cdd87acee9e067e7760dd4a423e4b3.png","width":1200,"height":630}}]},{"@context":"https://schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Investing & Trading Basics","item":"https://alysly.com/learn/"},{"@type":"ListItem","position":2,"name":"Level 0","item":"https://alysly.com/learn/#level-0"},{"@type":"ListItem","position":3,"name":"The Rule of 72: Estimating Doubling Time"}]},{"@context":"https://schema.org","@type":"Article","@id":"https://alysly.com/learn/rule-of-72/#entity","headline":"The Rule of 72: Estimating Doubling Time","description":"A rule of thumb for compounding: 72 divided by the annual return gives roughly the years until a sum doubles – with its limits and the exact calculation.","inLanguage":"en-US","mainEntityOfPage":"https://alysly.com/learn/rule-of-72/","image":[{"@type":"ImageObject","height":630,"url":"https://alysly.com/img/ta/rule-72-og.8b5d1ec892f31d3e7e2a53857c9c680766cdd87acee9e067e7760dd4a423e4b3.png","width":1200},{"@type":"ImageObject","height":520,"url":"https://alysly.com/img/ta/rule-72.54b02388c8fa29388f5913346396caf05e184b4fe4b7488dfb55098e3f346455.webp","width":1280}],"isPartOf":{"@type":"CreativeWorkSeries","name":"Investing & Trading Basics","url":"https://alysly.com/learn/"},"educationalLevel":"Level 0","author":{"@id":"https://alysly.com/#founder"},"publisher":{"@id":"https://alysly.com/#org"},"datePublished":"2026-07-13T11:24:42+02:00","dateModified":"2026-11-01T18:26:04+01:00"}],"notice":"© 2026 Alysly.com. Not investment advice. All data without guarantee. Financial information is analyzed and presented partly with AI assistance."}