Finance

Rule of 72: How Long to Double Your Money

Q: What exactly is the Rule of 72 and where does it come from?

The Rule of 72 is a mental math shortcut that estimates how many years it takes an investment to double in value under compound interest. The formula is simple: Years to double = 72 ÷ annual interest rate (%) . At 6%, that's 12 years. At 9%, it's 8 years. The rule traces back to at least 1494 , when Italian mathematician Luca Pacioli referenced it in Summa de Arithmetica , though some historians credit earlier Islamic mathematicians. The number 72 approximates 100 × ln(2) ≈ 69.3 but was chosen because it has more integer divisors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36), making mental division far cleaner. The often-quoted Einstein attribution — 'Compound interest is the eighth wonder of the world' — is unverified in his writings but remains one of finance's most enduring aphorisms.

Q: How accurate is the Rule of 72 compared to the exact formula?

The Rule of 72 is most accurate for rates between 6% and 10% , where the error is less than 1%. Outside that range, accuracy decreases. At 2% , the rule gives 36 years while the exact formula yields 35.0 — a 2.8% error. At 20% , the rule says 3.6 years; the exact answer is 3.8 years — about a 5% underestimate. At 50% , the rule gives 1.44 years versus the exact 1.71 years — a 16% error. The exact formula is: n = ln(2) ÷ ln(1 + r) , where r is the decimal rate (e.g., 0.08 for 8%). For rates below 3% or above 15%, use this calculator's exact result rather than the mental-math approximation.

Q: What if my investment returns vary year to year — does the rule still work?

The Rule of 72 assumes a constant annual rate . For volatile investments like stocks or mutual funds, you need the CAGR (Compound Annual Growth Rate) — the geometric average return — rather than the arithmetic average. Example: a fund returns +20%, −10%, +15%, +8%, +6% over five years. Arithmetic average = 7.8%, but CAGR = [(1.20 × 0.90 × 1.15 × 1.08 × 1.06)^(1/5)] − 1 ≈ 7.3% . Apply Rule of 72: 72 ÷ 7.3 ≈ 9.9 years to double. Using arithmetic average instead would falsely suggest 9.2 years. Always use CAGR when rates fluctuate — arithmetic averages systematically overstate real growth due to volatility drag.

Q: Does compound frequency (monthly vs. annual) affect the Rule of 72?

Yes — the Rule of 72 as classically stated assumes annual compounding . More frequent compounding accelerates growth. A 6% nominal rate compounded monthly has an effective annual rate (EAR) of (1 + 0.06/12)^12 − 1 ≈ 6.168% . Using EAR in the Rule of 72: 72 ÷ 6.168 ≈ 11.67 years versus 12 years with annual compounding — about 4 months faster. For savings accounts and CDs, always check whether the stated APR uses monthly, daily, or annual compounding, and use the APY (Annual Percentage Yield) — which already reflects compounding frequency — as your input to get accurate results.

Q: How does the Rule of 72 apply to debt and loans?

The rule cuts both ways: it applies to any compound growth , including debt. If you carry a credit card balance at 24% APR , your debt doubles in 72 ÷ 24 = 3 years if you make no payments. A student loan at 7% doubles in about 10.3 years. This reframing is psychologically powerful: the same math that grows your investments also grows what you owe. Financial advisors often use this to motivate debt payoff — eliminating a 20% credit card is a guaranteed 20% return, doubling your effective wealth protection every 3.6 years versus letting it compound against you.

Q: What rate of return do I need to double my money in a specific number of years?

Simply reverse the formula : Required rate = 72 ÷ target years . Want to double in 5 years ? You need roughly 14.4% annually (exact: 14.87%). In 10 years ? About 7.2% (exact: 7.18%). In 15 years ? Approximately 4.8% (exact: 4.73%). This reverse application is invaluable for goal-based investing — if your retirement goal requires doubling your portfolio in 8 years, you know you need roughly a 9% annual return , which helps you select appropriate asset allocation (likely 70–80% equities historically needed to sustain that rate net of fees).

Q: Why do small differences in annual rate matter so much over long periods?

Because of exponential compounding , even 1–2 percentage points create massive differences over decades. Consider $10,000 invested for 30 years: at 6% it grows to ~$57,400 (doubles ~2.9 times); at 8% it becomes ~$100,600 (doubles ~3.3 times); at 10% it reaches ~$174,500 (doubles ~3.7 times). The difference between 6% and 10% is not 67% more money — it's 204% more money . This is why expense ratios on investment funds matter so much: a fund charging 1% instead of 0.1% in fees costs you nearly a full percentage point of net return annually — and by the Rule of 72, that shifts your doubling time from ~7.6 years to ~8.3 years, compounding the gap every cycle.

Use the Rule of 72 to find how long it takes to double your money. Enter any annual rate and get exact years, tripling & quadrupling times.

U.S. Securities and Exchange Commission data · July 2026 · Martín Rodríguez

More info

Formula verified by automated tests
Private — runs on your device

Calculator Free · Private

Edited by: Martín Rodríguez (editorial policy )

Suggest an improvement

🧮 Keep calculating

Loan Payment CalculatorCalculate your monthly loan payment, total interest and amortization schedule. Works for personal loans, auto loans and mortgages.Mortgage Payoff Calculator (Extra Payment)See how much time and interest an extra monthly mortgage payment saves you. Free, no sign-up needed and instant results.US Inflation Calculator (CPI-U)Calculate the value of a dollar over time with the US CPI. See what any amount from 1913 to 2025 is worth today, the total inflation, and the average annual inflation rate between any two years.ROI Calculator — Total Return & Annualized Rate (CAGR)Enter your initial investment and final value to get total return on investment %, net profit, and annualized ROI (CAGR). Free, no sign-up.

Want to change something?Edit any field and calculate again.

Instant resultIt recalculates in your browser, no page reload.

Fast and transparent

How to use this calculator

Follow this tool’s steps, then review its formula, assumptions, and limits below.

Step by step

Enter annual compound rateEnter annual compound rate (%) (e.g., 8).

Enter initial capitalEnter initial capital (optional) (e.g., 1000).

Click CalculatePress "Calculate" to get the result instantly.

The Rule of 72 is a classic US personal-finance heuristic (taught by Investor.gov from the SEC, the CFPB / Consumer Financial Protection Bureau's financial education materials, and AP Economics): divide 72 by your annual compound interest rate (APY) to estimate years to double your money. At 8% APY → ~9 years; at 6% → 12 years; at 12% → 6 years. Pacioli first wrote it down in 1494, but in the US today it's the go-to shortcut for comparing a high-yield savings account, an S&P 500 index fund in a 401(k), a Roth IRA, US Treasury bonds, or a CD. This tool also applies the exact log formula n = ln(2) ÷ ln(1+r) and shows tripling (Rule of 114) and quadrupling (Rule of 144) times. Works equally for inflation — if the BLS reports 4% CPI, your dollar's purchasing power halves in 18 years.

When to use this calculator

Comparing a CD vs. an index fund — You're deciding between a 4.5% 5-year CD and a broad index fund averaging 10% annually. The Rule of 72 instantly shows you: the CD doubles your money in 16 years (72 ÷ 4.5), while the index fund doubles it in 7.2 years (72 ÷ 10). Over a 30-year horizon, the index fund doubles roughly four times versus fewer than two for the CD — a stark visual for long-term decision-making.
Understanding the true cost of inflation — With the US CPI running around 4% annually, the Rule of 72 tells you your purchasing power halves in just 18 years (72 ÷ 4). If you keep $50,000 in a non-interest-bearing checking account today, it will have the buying power of only $25,000 by 2042. This single insight motivates moving idle cash into at least a high-yield savings account or Treasury bills currently yielding above 5%.
Retirement planning for a 30-year-old — A 30-year-old invests $20,000 in a diversified portfolio targeting a 7% average annual return (a common post-fee estimate for balanced funds). Rule of 72: doubles every 10.3 years. By age 60, that $20,000 doubles roughly three times → $20,000 → $40,000 → $80,000 → $160,000, even without adding another dollar. Starting at 40 instead? Only two doublings → $80,000. The cost of waiting 10 years: $80,000 in lost growth.
Evaluating a real estate syndication pitch — A sponsor promises a 12% annual return on a commercial real estate deal. Rule of 72 says your investment doubles in 6 years. The exact formula confirms 6.12 years. Armed with this, you can quickly compare it against a REIT averaging 9% (doubles in 8 years) or a private equity fund at 15% (doubles in 4.8 years). Concrete timelines make abstract percentages much easier to evaluate during due diligence.
Teaching compound interest to a teenager — A 16-year-old has $1,000 saved. Investing it at 8% in a Roth IRA, the Rule of 72 shows it doubles every 9 years: $1,000 → $2,000 at 25 → $4,000 at 34 → $8,000 at 43 → $16,000 at 52, all from the original $1,000. Contrast that with the same $1,000 invested at age 26 — it only reaches $8,000 by age 52. This side-by-side comparison is one of the most compelling financial literacy lessons available.
Stress-testing a high-yield investment claim — An acquaintance claims a crypto-adjacent fund delivers 36% annually. Rule of 72 says that doubles money every 2 years. In 10 years, $10,000 would become $573,000. The implausibility of those numbers becomes obvious when you apply the rule — legitimate regulated funds rarely sustain above 15–20% long-term. The Rule of 72 is an instant sanity check against unrealistic pitches.
Planning a college savings fund — Parents invest $15,000 in a 529 plan today with a child aged 6, targeting 6% annual returns. Rule of 72: doubles in 12 years — just in time for college at age 18. Without adding contributions, that $15,000 grows to roughly $30,200 by the exact formula. They can use this projection to calculate how much additional monthly contribution is needed to reach a $60,000 target, making abstract savings goals concrete and actionable.
Estimating national debt or GDP growth doubling time — The Rule of 72 isn't just for personal finance. If the US national debt grows at roughly 6% per year, it doubles in 12 years. If a country's GDP grows at 3%, it doubles in 24 years. Economists, journalists, and policy analysts routinely use this shortcut to communicate the long-term implications of growth rates to general audiences without requiring a spreadsheet.

Years to double, triple, quadruple and 10x by annual rate

Rule-of-72 family: double = 72/rate, triple = 114/rate, quadruple = 144/rate, 10x = 231/rate.

Annual rate	Double (Rule of 72)	Triple (114)	Quadruple (144)	10x (231)
2%	36 yrs	57 yrs	72 yrs	115.5 yrs
4%	18 yrs	28.5 yrs	36 yrs	57.8 yrs
6%	12 yrs	19 yrs	24 yrs	38.5 yrs
8%	9 yrs	14.3 yrs	18 yrs	28.9 yrs
10%	7.2 yrs	11.4 yrs	14.4 yrs	23.1 yrs
12%	6 yrs	9.5 yrs	12 yrs	19.3 yrs
15%	4.8 yrs	7.6 yrs	9.6 yrs	15.4 yrs
20%	3.6 yrs	5.7 yrs	7.2 yrs	11.6 yrs

Each rule number is 100 × ln(multiple): ln(2)≈69.3→72, ln(3)≈109.9→114, ln(4)≈138.6→144, ln(10)≈230.3→231. Most accurate between 6% and 10%. For exact values use n = ln(multiple) ÷ ln(1+r). Source: SEC / Investor.gov compound-interest education.

How it works

What Is the Rule of 72

The Rule of 72 is a mathematical approximation for mentally calculating years for an investment to double with compound interest. The formula:

Years to double = 72 / annual rate (%)

Example: you invest at 6% annual. 72 / 6 = 12 years. Your money doubles in 12 years.

Why 72 Works

The exact formula is n = ln(2) / ln(1+r). Since ln(2) ≈ 0.693, and for typical rates (4-12%) ln(1+r) ≈ r, then n ≈ 0.693 / r = 69.3 / r%. But 72 has many integer divisors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36), making it preferred for mental math.

Annual rate	Rule of 72	Exact formula	Difference
2%	36 years	35.00	+1.0
4%	18 years	17.67	+0.33
6%	12 years	11.90	+0.10
8%	9 years	9.01	−0.01
10%	7.2 years	7.27	−0.07
12%	6 years	6.12	−0.12
15%	4.8 years	4.96	−0.16
20%	3.6 years	3.80	−0.20

Conclusion: the Rule of 72 is very accurate between 6% and 10%. For very low rates use 70, for high rates use 76-78.

Variants: Rule of 69, 70, and 72

Rule of 69: more accurate for continuous interest (using e).

Rule of 70: good general compromise, used in demographics.

Rule of 72: most popular because 72 divides easily mentally.

The Power of Compound Interest

Classic question: if you had $1 at birth invested at 7%, how much at age 72?

At 10 years (Rule 72): $2 — first doubling.

At 20 years: $4.

At 30 years: $8.

At 40 years: $16.

At 50 years: $32.

At 60 years: $64.

At 70 years: $128.

From $1 to $128 just by waiting and reinvesting. Compound power is exponential.

To Triple and Quadruple

Triple: use the Rule of 114 (114/rate). Example: at 8% = 14.25 years.

Quadruple: Rule of 144 (144/rate). Example: at 8% = 18 years (two doublings).

10x: Rule of 231. At 8% = 28.9 years.

Common Investment Comparisons (years to double)

Instrument	Historical annual return	Years to double
Checking account	0%	∞ (loses to inflation)
10-year US Treasury	4%	18 years
S&P 500 (historical)	10%	7.2 years
Nasdaq (last 20 years)	13%	5.5 years
Bitcoin (2011-2024)	60-80%	~1 year
Global real estate	6%	12 years

Practical Applications

1. Compare 2 investments:

Option A: 6% annual → doubles in 12 years.

Option B: 9% annual → doubles in 8 years.

At 40 years, A multiplies by 10, B by 32.

2. Detect unrealistic promises:

Someone promises 25% annually. Doubles in 3 years. Sustainable at 10 years? Multiplies by 10. Ponzi schemes often promise this and collapse.

3. Inflation:

With 8% annual inflation, your purchasing power is cut in half in 9 years if you don't invest.

Exact Formula

n = ln(2) / ln(1 + r)

Where r is the rate as a decimal. Examples:

r = 0.08 → ln(2)/ln(1.08) = 0.693/0.0770 = 9.006 years.

r = 0.12 → ln(2)/ln(1.12) = 0.693/0.1133 = 6.116 years.

Common Mistakes

1. Applying to simple interest: the Rule of 72 only works with compound interest. For simple interest, doubling time is 100 / rate.
2. Forgetting inflation: if you want to double your purchasing power, use the real rate (nominal rate − inflation).
3. Very high or low rates: for rates <2% or >20%, the approximation loses accuracy.
4. Rate changes: the rule assumes a constant rate. In real life, returns vary year to year.

Example: investing $10,000 at 8% annual

Initial capital: $10,000.

Annual compound rate: 8%.

Rule of 72: 72 / 8 = 9 years.

Exact formula: ln(2) / ln(1.08) = 9.006 years.

Result: your money becomes $20,000 in approximately 9 years.

To triple ($30,000): ln(3) / ln(1.08) = 14.3 years.

To quadruple ($40,000): 18 years (two doublings).

At 8% APY, $10,000 becomes $20,000 in 9 years, $40,000 in 18 years, and $80,000 in 27 years — close to the S&P 500's long-term US historical return inside a Roth IRA or 401(k).

Disclaimer: Informational estimate. Actual rates, fees, and terms depend on the provider and contract; compare official documents before deciding.

Frequently asked questions

What exactly is the Rule of 72 and where does it come from?

The Rule of 72 is a mental math shortcut that estimates how many years it takes an investment to double in value under compound interest. The formula is simple: Years to double = 72 ÷ annual interest rate (%). At 6%, that's 12 years. At 9%, it's 8 years. The rule traces back to at least 1494, when Italian mathematician Luca Pacioli referenced it in Summa de Arithmetica, though some historians credit earlier Islamic mathematicians. The number 72 approximates 100 × ln(2) ≈ 69.3 but was chosen because it has more integer divisors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36), making mental division far cleaner. The often-quoted Einstein attribution — 'Compound interest is the eighth wonder of the world' — is unverified in his writings but remains one of finance's most enduring aphorisms.

How accurate is the Rule of 72 compared to the exact formula?

The Rule of 72 is most accurate for rates between 6% and 10%, where the error is less than 1%. Outside that range, accuracy decreases. At 2%, the rule gives 36 years while the exact formula yields 35.0 — a 2.8% error. At 20%, the rule says 3.6 years; the exact answer is 3.8 years — about a 5% underestimate. At 50%, the rule gives 1.44 years versus the exact 1.71 years — a 16% error. The exact formula is: n = ln(2) ÷ ln(1 + r), where r is the decimal rate (e.g., 0.08 for 8%). For rates below 3% or above 15%, use this calculator's exact result rather than the mental-math approximation.

What's the difference between Rule of 72, Rule of 70, and Rule of 69?

All three estimate doubling time but suit different contexts. Rule of 70 is preferred for demography and economics — population growth, GDP — because rates tend to be low (1–4%) and 70 divides evenly by those values. Rule of 69 (or 69.3) is technically the most mathematically precise for continuous compounding, since ln(2) = 0.6931. Rule of 72 wins for annual compound interest calculations (the most common financial scenario) because 72's divisibility by 8 and 9 — rates common in investing — makes mental math effortless. In practice, many financial advisors default to 72 for all three contexts simply for convenience.

Can I use the Rule of 72 to calculate inflation's impact on purchasing power?

Absolutely — and it's one of the most eye-opening applications. The rule works in reverse: if inflation runs at 4% annually, your cash purchasing power halves in 18 years (72 ÷ 4). At 8% inflation, it halves in just 9 years. This means $100,000 in a non-interest-bearing account loses half its real value in under two decades. To protect yourself, you need investments whose returns exceed inflation. The real rate of return = nominal rate − inflation rate. If your portfolio earns 7% and inflation is 3%, your real doubling time is 72 ÷ 4 = 18 years, not 72 ÷ 7 = 10.3 years.

How do I calculate tripling, quadrupling, or 10x time?

The same logic extends with different numerators based on the natural log of your target multiple: Tripling: use the Rule of 114 — 114 ÷ rate. At 8%: 14.25 years (exact: 14.27). Quadrupling: use the Rule of 144 — 144 ÷ rate. At 8%: 18 years (exact: 18.01) — equivalently, just double the doubling time. 10x: use the Rule of 231 — 231 ÷ rate. At 8%: 28.9 years (exact: 29.9). These are derived from: n = ln(target) ÷ ln(1 + r). Multiply ln(target) × 100 to get your rule number: ln(3) ≈ 109.9, ln(4) ≈ 138.6, ln(10) ≈ 230.3.

What if my investment returns vary year to year — does the rule still work?

The Rule of 72 assumes a constant annual rate. For volatile investments like stocks or mutual funds, you need the CAGR (Compound Annual Growth Rate) — the geometric average return — rather than the arithmetic average. Example: a fund returns +20%, −10%, +15%, +8%, +6% over five years. Arithmetic average = 7.8%, but CAGR = [(1.20 × 0.90 × 1.15 × 1.08 × 1.06)^(1/5)] − 1 ≈ 7.3%. Apply Rule of 72: 72 ÷ 7.3 ≈ 9.9 years to double. Using arithmetic average instead would falsely suggest 9.2 years. Always use CAGR when rates fluctuate — arithmetic averages systematically overstate real growth due to volatility drag.

Does compound frequency (monthly vs. annual) affect the Rule of 72?

Yes — the Rule of 72 as classically stated assumes annual compounding. More frequent compounding accelerates growth. A 6% nominal rate compounded monthly has an effective annual rate (EAR) of (1 + 0.06/12)^12 − 1 ≈ 6.168%. Using EAR in the Rule of 72: 72 ÷ 6.168 ≈ 11.67 years versus 12 years with annual compounding — about 4 months faster. For savings accounts and CDs, always check whether the stated APR uses monthly, daily, or annual compounding, and use the APY (Annual Percentage Yield) — which already reflects compounding frequency — as your input to get accurate results.

How does the Rule of 72 apply to debt and loans?

The rule cuts both ways: it applies to any compound growth, including debt. If you carry a credit card balance at 24% APR, your debt doubles in 72 ÷ 24 = 3 years if you make no payments. A student loan at 7% doubles in about 10.3 years. This reframing is psychologically powerful: the same math that grows your investments also grows what you owe. Financial advisors often use this to motivate debt payoff — eliminating a 20% credit card is a guaranteed 20% return, doubling your effective wealth protection every 3.6 years versus letting it compound against you.

What rate of return do I need to double my money in a specific number of years?

Simply reverse the formula: Required rate = 72 ÷ target years. Want to double in 5 years? You need roughly 14.4% annually (exact: 14.87%). In 10 years? About 7.2% (exact: 7.18%). In 15 years? Approximately 4.8% (exact: 4.73%). This reverse application is invaluable for goal-based investing — if your retirement goal requires doubling your portfolio in 8 years, you know you need roughly a 9% annual return, which helps you select appropriate asset allocation (likely 70–80% equities historically needed to sustain that rate net of fees).

Why do small differences in annual rate matter so much over long periods?

Because of exponential compounding, even 1–2 percentage points create massive differences over decades. Consider $10,000 invested for 30 years: at 6% it grows to ~$57,400 (doubles ~2.9 times); at 8% it becomes ~$100,600 (doubles ~3.3 times); at 10% it reaches ~$174,500 (doubles ~3.7 times). The difference between 6% and 10% is not 67% more money — it's 204% more money. This is why expense ratios on investment funds matter so much: a fund charging 1% instead of 0.1% in fees costs you nearly a full percentage point of net return annually — and by the Rule of 72, that shifts your doubling time from ~7.6 years to ~8.3 years, compounding the gap every cycle.

How do taxes affect the Rule of 72 calculation?

Taxes reduce your effective after-tax return, extending your real doubling time. If your investment earns 8% annually but you pay 25% in capital gains taxes each year on gains (common in taxable brokerage accounts with annual rebalancing), your after-tax return drops to 6%, pushing your doubling time from 9 to 12 years. Tax-advantaged accounts — 401(k), IRA, Roth IRA — let compound interest work on the full pre-tax or tax-free return. In a Roth IRA at 8%, you double every 9 years tax-free; in a taxable account at the same gross return, you might effectively double every 11–12 years after annual tax drag. Always apply the Rule of 72 to your after-tax, after-fee net return for realistic planning.

Is the Rule of 72 useful for business and non-financial growth rates?

Widely so. Any metric growing at a compound rate can be analyzed with Rule of 72: Company revenue: a SaaS business growing at 36% annually doubles ARR in 2 years. Population: a city growing at 3% doubles in 24 years. Website traffic: growing SEO traffic at 6% monthly doubles in 12 months (72 ÷ 6). Energy consumption: if global energy use grows 2% annually, it doubles in 36 years, helping engineers size infrastructure. Carbon emissions: policymakers use Rule of 70/72 to model reduction timelines. Anywhere a percentage growth rate applies consistently over time, the Rule of 72 translates abstract rates into tangible, relatable timelines that non-specialists can immediately grasp.

Sources & references

SEC / Investor.gov - Compound Interest Calculator & Investor Education — U.S. Securities and Exchange Commission
Consumer Financial Protection Bureau - Compound Interest Explained — Consumer Financial Protection Bureau
Federal Reserve / FRED - Long-Run Returns: S&P 500 & US Treasuries — Federal Reserve Bank of St. Louis
Rule of 72 - Investopedia (US personal finance reference) — Investopedia

Methodology & trust

Editorial

Finance calculator with its formula verified automatically against SEC / Investor.gov - Compound Interest Calculator & Investor Education, per our editorial policy and methodology.

Updates

Updated: July 2026. Parameters are verified periodically against the cited sources.

Privacy

Calculations run 100% in your browser. We do not store or transmit your data.

Limitations

Indicative results. For critical decisions, consult a professional.

📌 How to cite this calculator

Rodríguez, M. (2026). Rule of 72: How Long to Double Your Money. Hacé Cuentas. https://hacecuentas.com/en/rule-of-72-calculator

Content licensed under CC-BY 4.0 — reuse it citing the source with a link to Hacé Cuentas.

✉️ Report an error in this calculator