Finance Tools

Rule of 72 Calculator

Calculate how long it takes your investment to double

Doubling Time Calculator

Enter an interest rate to find how long it takes to double your money

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Annual return on investment

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Required Rate Calculator

Find the interest rate needed to double your money in a specific time

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Rate Comparison

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Rate Rule of 72 Exact Accuracy
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Growth Visualization

See how your money grows through multiple doublings

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Rule of 72 Reference

Formulas, variations, and background

The Rule of 72
Years to Double = 72 ÷ Interest Rate (%)
Exact Formula (Compound Interest)
Years = ln(2) ÷ ln(1 + r) ≈ 69.3 ÷ r
Why 72?
Mathematical Basis

The natural log of 2 is approximately 0.693, which means the exact multiplier should be 69.3. However, 72 is used because:

  • 72 has more divisors (1,2,3,4,6,8,9,12,18,24,36,72)
  • Easier mental math
  • More accurate for typical rates (6-10%)
Accuracy Range

The Rule of 72 is most accurate between 6% and 10%. For rates outside this range:

  • Low rates (1-5%): Use Rule of 69 or 70
  • High rates (>20%): Use Rule of 78
Rule Variations
Rule Formula Best For
Rule of 69 69 ÷ rate Continuous compounding
Rule of 70 70 ÷ rate Low rates (2-5%)
Rule of 72 72 ÷ rate Medium rates (6-10%)
Rule of 78 78 ÷ rate High rates (>20%)
Practical Applications
Investment Planning
  • Estimate retirement growth
  • Compare investment options
  • Set realistic expectations
Inflation Impact
  • See how fast prices double
  • 3% inflation = doubles in 24 years
  • Compare to wage growth
Debt Analysis
  • See how fast debt grows
  • Credit card at 18% = doubles in 4 years
  • Motivates faster repayment
Historical Background
First Documented Use

Luca Pacioli (1494) in "Summa de Arithmetica" - the same book that introduced double-entry bookkeeping

Einstein Quote (Attributed)

"Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it."

Understanding the Rule of 72

Quick Mental Math

The Rule of 72 lets you estimate doubling time in your head.

  • 6% return → 72÷6 = 12 years
  • 8% return → 72÷8 = 9 years
  • 12% return → 72÷12 = 6 years
Works Both Ways

The rule works for any exponential growth or decay.

  • Investments doubling
  • Debt accumulating
  • Inflation eroding value
  • Population growth
Power of Compounding

Multiple doublings lead to dramatic growth.

  • 1 doubling: 2x original
  • 3 doublings: 8x original
  • 5 doublings: 32x original
  • 10 doublings: 1,024x original