What is the rule of 72?
Answer
Divide 72 by your rate to get years to double.
The rule of 72 is a back-of-the-napkin formula: years to double = 72 ÷ annual return rate. At 8%, your money doubles in about 9 years. At 6%, it takes 12. At 12%, just 6.
Interactive tool · Free · Updated for 2026
Rule of 72 Calculator
See how long until your money doubles — and the multiples that compound after that.
The rule of 72 is the fastest mental math in personal finance: divide 72 by your annual return to see doubling time. This calculator shows the rule, the exact log-math answer, and the multiples that follow.
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4.9 / 5 · 980 ratingsThe fastest mental math in personal financeUsed to estimate doubling time across rates
Live calculation
runs locallyRule of 72
9.0 yrs
to double
Exact (log)
9.01 yrs
precise math
Approximation error
-0.07%
rule vs exact
Doubles to
$20.0K
at first doubling
Headline
Doubling time
9.0 yrs
rule of 72
Headline
In 10 years
$21.6K
compound value
In 20 years
$46.6K
two doublings-ish
In 30 years
$100.6K
long-arc total
Compounding curve
Your money over 40 years
Multiples & milestones
When your money hits each multiple.
Multiple
Years
Value
2×
9.0 yrs
$20.0K
4×
18.0 yrs
$40.0K
8×
27.0 yrs
$80.0K
16×
36.0 yrs
$160.0K
Quick Answers
Rule of 72, in 30 seconds.
Direct answers to the most common questions, in plain language. Skim if you're in a hurry; dig deeper below.
How accurate is it?
Answer
Surprisingly accurate for rates between 4% and 15%.
Within about 1% of the exact answer for typical investment rates. At very high rates (>20%) it slightly overshoots; at very low rates (<3%) it slightly underestimates. For mental math, it is good enough.
Does the rule of 72 work for debt?
Answer
Yes — it tells you how fast debt doubles.
Run the same math against credit-card debt. A 24% APR balance doubles in 3 years if you do not pay it down. A 7% student loan doubles in just over a decade. The doubling logic is exactly the same — just running against you.
Why 72 and not 70?
Answer
72 has more divisors — easier mental math.
72 is divisible by 2, 3, 4, 6, 8, 9, 12 — which makes it easy to divide by common interest rates. The exact "rule" is closer to 69.3 (ln 2), so 70 is slightly more accurate at low rates and 72 is more accurate around 8%.
How it works
How rule of 72 works.
The mechanics in short answers — no jargon, no upsell.
01
Pick your annual rate.
Real, after-inflation return is what most planners use. Historical S&P 500 real return is around 7%; bonds are 1–3%; high-yield savings is roughly inflation.
02
Divide 72 by the rate.
At 8%: 72 ÷ 8 = 9 years to double. At 12%: 72 ÷ 12 = 6 years. The relationship is inverse — double the rate, halve the time.
03
Stack the doublings.
Each doubling does not slow down; it accelerates. $10k → $20k → $40k → $80k. The third doubling adds more dollars than the first two combined.
04
Match doublings to age.
Most retirement portfolios need 3–4 doublings between starting work and retiring. Each year you delay starting costs a full doubling at the end.
How to use
Four steps. About 20 seconds.
Designed so anyone can model their situation in under a minute, with or without a finance background.
- Step 1Enter starting principalYour current investment or savings balance.
- Step 2Set expected returnUse real (after-inflation) return for planning — typically 5–7%.
- Step 3See doubling timeYears to double, plus the exact compound math beside it.
- Step 4Stack future doublingsSee when you hit 2×, 4×, 8× — the curve steepens fast.
Benefits
Why this matters.
See compounding intuitively
Doubling time turns abstract rates into concrete years.
Compare any two rates
Stocks, bonds, savings, real estate — see how their doubling times stack up.
Apply to debt too
Run the same math against credit cards to see why a balance balloons.
Plan retirement milestones
See when your portfolio doubles and triples — and how that lines up with retirement.
Sanity-check projections
A fund promising "doubling in 4 years" implies an 18% return. Now you know.
Multi-double projection
See the second and third doubling — when the curve really steepens.
FAQ
Rule of 72, answered.
Everything you might ask before, during, or after using this tool.
Written for borrowers, not bankersPlain-language, jargon-freeReviewed quarterly
Is the rule of 72 still accurate at low interest rates?
It slightly underestimates doubling time at very low rates (under 3%). The exact formula is years = ln(2) / ln(1 + rate) ≈ 69.3 / rate. At rates below 3%, using 69 or 70 instead of 72 is more accurate. For investing-level rates (5–12%), 72 is excellent.
Does this account for inflation?
Not directly — but you can. Plug in real return (nominal return minus inflation) instead of nominal return. That gives you the doubling time in real purchasing power, which is usually the more honest number.
How do I use it for a 401(k) projection?
Estimate your real annual return (7% historically for diversified equities). Divide 72 by that. That is how often your balance doubles. From there, count doublings between now and your retirement age to ballpark the final amount.
What rate should I assume for stocks?
S&P 500 long-run real return has averaged about 7% (about 10% nominal minus 3% inflation). Use 5% for a conservative planning case, 7% for base case, 9% for optimistic. The math compounds either way.
How does this apply to debt?
A balance accruing 24% APR doubles in 3 years if untouched. A 7% student loan doubles in 10. Apply the same formula — debt compounds against you exactly the way investments compound for you.
Is there a "rule of 144" for tripling?
Sort of — divide 114 by the rate for tripling time. Divide 144 for quadrupling (which is just two doublings). The math holds with any growth multiple, just with a different magic number.
Why is doubling time inversely proportional?
Mathematically, doubling time depends on ln(2) / ln(1+r), which behaves almost like 1/r for small r. That is why 72 ÷ rate works — it is an approximation of the exact log relationship that holds across normal investing rates.
Does this work for monthly compounding?
The rule assumes annual compounding. Monthly compounding gives slightly faster doubling — typically 1–3% faster than the rule of 72 predicts at typical investment rates. The error is small enough that 72 is still a reasonable approximation.
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Why 72 — the math behind the magic
The exact formula for doubling time is years = ln(2) / ln(1+r). For small r, that simplifies to about 69.3 / r. Round to 72 because it is divisible by more numbers, and you have a fraction-free mental shortcut.
At 8%, 72 ÷ 8 = 9. Exact: 9.006. Off by 0.07%. Good enough for napkins.
Stacking doublings is where the magic happens
One doubling looks ordinary. Three doublings is 8×. Four doublings is 16×. By the time you stack five or six, the absolute dollars compounding in the last decade dwarf everything before.
This is why starting in your 20s vs 30s matters so much — you literally get one more doubling. That doubling is the largest in absolute terms.
Real return, not nominal — for honest planning
Plug in your nominal return and you get nominal doubling. Plug in real return (return minus inflation) and you get how often your purchasing power doubles. The second number is the one that matters.
At 7% real return, money doubles every ~10 years in actual purchasing power. That is the number to plan around.
When the rule works against you
Credit-card APRs of 22–28% mean unpaid balances double in 2.5–3 years. A medical-debt collection growing at 18% doubles in 4 years.
The same compounding that builds wealth from a 7% portfolio destroys it from a 24% revolving balance. The mechanism is identical.
Common rule-of-72 mistakes
- Using nominal return instead of real return for retirement planning.
- Assuming the rule holds for very short horizons (it does, but with caveats).
- Forgetting that fees compound against you the same way.
- Ignoring the rule when comparing investment options — a 1% fee turns a 10-year doubling into ~12 years.
- Treating it as exact rather than a 1–2% approximation.
Trust & transparency
How this tool behaves, and what it isn't.
Two short notes worth reading before you trust any number on this page.
Privacy
Calculations run locally in your browser.
Your loan amount, rate, and prepayment inputs never leave your device. No accounts, no cookies on your numbers, no analytics on the values you type. Disconnect from the internet and it still works.
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- No data stored or sent
- Works offline
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Disclaimer
Lazysmirk is a tools platform, not a financial institution.
We are not a bank, NBFC, advisor, broker, or distributor of any financial product. The numbers shown here are estimates for educational purposes only, based on the inputs you provide.
Results are not financial, legal, or tax advice. Please consult a qualified professional before any decision about your loan, investments, or personal finances. Actual loan terms and charges depend on your bank and individual circumstances.