Rule of 72 Calculator How Long to Double Your Money?
Use the Rule of 72 to estimate how long it takes to double your money at any interest rate. Compare the Rule of 72, Rule of 69.3, Rule of 70, and the exact formula side by side. Solve for years or for rate.
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Currency
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Rule of 72
Solve For
%
Enter the annual growth or interest rate. Rule of 72 answers: 72 ÷ rate.
yrs
Enter the number of years. Rule of 72 answers: 72 ÷ years.
freq
Affects the exact calculation. Rule of 72 always uses the nominal annual rate.
◆
Enter any amount to see the doubled, tripled, and quadrupled values.
Years to Double
—yrs
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Exact Answer
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Rule of 69.3
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All Approximations vs Exact
RuleResultFormulaError vs exact
Rule of 72———
Rule of 70———
Rule of 69.3———
Exact formula——0.000%
Rule of 72
—
years
Exact Answer
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years
Compounding
—
frequency
Triple Time
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years to 3x (exact)
Quadruple Time
—
years to 4x (exact)
Doubled Amount
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starting × 2
Full Breakdown
Growth Curve to Doubling (and Beyond)
Exact growth
Double target
Years to Double at Common Rates (Rule of 72)
Years to Double by Rate
Rate (%)
Rule of 72
Rule of 70
Rule of 69.3
Exact (Annual)
Error (R72 vs Exact)
Rate Needed to Double in N Years
Years
Rule of 72 Rate
Exact Rate (Annual)
Error
Note: The Rule of 72 is a mental math shortcut, not a financial product. It assumes annual compounding on the nominal rate. Exact calculations use logarithms and the selected compounding frequency. Results are mathematical estimates and do not account for taxes, fees, inflation, or varying returns.
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▶ Key Notes
Rule of 72 is most accurate for rates between 6% and 10%
Rule of 69.3 is more accurate mathematically but less convenient
Continuous compounding makes 69.3 exact, not approximate
Works for any doubling scenario including inflation and debt
Tripling uses Rule of 114; quadrupling uses Rule of 144
The Rule of 72 is a mental shortcut for estimating how long it takes an investment to double in value at a fixed annual return. Divide 72 by the annual interest rate and the result is approximately the number of years required. For example, at 8% per year, money doubles in approximately 72 ÷ 8 = 9 years.
Rule
Formula (years)
Formula (rate)
Most accurate range
Rule of 72
72 ÷ rate
72 ÷ years
6% to 10%
Rule of 70
70 ÷ rate
70 ÷ years
2% to 5%
Rule of 69.3
69.3 ÷ rate
69.3 ÷ years
All rates (continuous)
Exact (annual)
ln(2) ÷ ln(1 + r)
2^(1/n) − 1
Always exact
Why 72 and not 69.3?
The mathematically precise constant for continuous compounding is ln(2) ≈ 0.693, which gives the Rule of 69.3. However, 72 is a more useful practical shortcut because it has more divisors (1, 2, 3, 4, 6, 8, 9, 12) than 69 or 70, making mental arithmetic much easier at common interest rates. At 6%, 8%, 9%, and 12%, the Rule of 72 produces whole-number answers. The slight overestimate from using 72 instead of 69.3 is negligible for most planning purposes at rates between 4% and 15%.
Compounding frequency and doubling time
More frequent compounding reduces the time needed to double at the same nominal rate because interest compounds on interest more often. The Rule of 72 uses the nominal annual rate and implicitly assumes annual compounding. The exact calculation adjusts for quarterly, monthly, or continuous compounding. The difference is small at low rates but grows at higher rates.
Using the Rule of 72 for inflation and debt
The Rule of 72 applies to any exponential growth or decay. For inflation, dividing 72 by the inflation rate gives the approximate number of years before purchasing power halves. At 4% inflation, purchasing power halves in approximately 18 years. For debt, the same rule shows how quickly a balance doubles if interest accrues without repayment.
Frequently Asked Questions
What is the Rule of 72?+
The Rule of 72 estimates the number of years required to double an investment by dividing 72 by the annual interest rate. It is a mental arithmetic shortcut that works best at interest rates between 6% and 10% and assumes annual compounding. For example, at 9% the answer is 72 ÷ 9 = 8 years, and the exact answer is ln(2) ÷ ln(1.09) = 8.04 years.
Why is the Rule of 72 not perfectly accurate?+
The Rule of 72 is an approximation of the exact formula ln(2) ÷ ln(1 + r), which involves natural logarithms. The number 72 was chosen because it produces convenient whole-number results for common rates and is divisible by more integers than 69 or 70. At very low rates (below 2%) or very high rates (above 20%), the error increases and the exact formula should be used.
Does compounding frequency affect the Rule of 72?+
The Rule of 72 always uses the nominal annual rate and implicitly assumes annual compounding. If interest compounds more frequently (monthly or continuously), the actual doubling time is shorter than the Rule of 72 estimate. For continuous compounding, the exact relationship is t = ln(2) ÷ r, where r is the nominal rate. This makes 69.3 the exact constant for continuous compounding, not an approximation.
How do I use the Rule of 72 for inflation?+
Replace the investment return with the inflation rate. The result is approximately the number of years before a sum of money loses half its purchasing power. At 3% inflation, purchasing power halves in roughly 72 ÷ 3 = 24 years. This works because inflation compounds in the same mathematical way as investment growth, just in reverse from the perspective of real purchasing power.
What are the rules for tripling and quadrupling?+
The Rule of 114 estimates years to triple (114 ÷ rate) and the Rule of 144 estimates years to quadruple (144 ÷ rate). These come from the same logarithmic relationship: ln(3) ≈ 1.099 and ln(4) ≈ 1.386, which give approximate constants of 110 to 115 and 138 to 144 depending on the rate range targeted. The exact formulas are ln(3) ÷ ln(1 + r) and ln(4) ÷ ln(1 + r) respectively.
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