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Calculate how long it takes for exponential growth to double using exact formula or Rule of 72
Annual percentage rate for investments, or per-period rate
The Rule of 72 is a quick mental math shortcut: divide 72 by the percentage rate to estimate doubling time.
Doubling time is the period it takes for a quantity growing exponentially to double in size. For example, if a population or investment doubles every 10 years, the doubling time is 10 years.
Use the formula: Doubling Time = ln(2) / ln(1 + r), where r is the growth rate as a decimal (7% = 0.07). This gives the exact time for discrete compound growth.
The Rule of 72 is a mental math shortcut: Doubling Time ≈ 72 / rate%. It's remarkably accurate for growth rates between 6% and 10%, making it perfect for quick investment calculations.
The Rule of 72 works best for rates between 6% and 10%. For very low rates (under 5%), use Rule of 70. For very high rates (over 20%), the approximation becomes less accurate.
Absolutely! Enter your annual interest rate to find how long until your money doubles. For example, at 7% annual return, your investment doubles in about 10.24 years (or ~10 years using Rule of 72).
Population doubling works the same way. A population growing at 2% per year doubles in about 35 years. Historical world population doubled roughly every 40-50 years during the 20th century.
They're inverses! Doubling time applies to growth; half-life applies to decay. The formulas are similar but use opposite signs. Doubling time uses ln(2)/ln(1+r), while half-life uses ln(2)/k for decay constant k.
If the growth rate changes over time, use the average growth rate or calculate doubling time for different periods separately. Real investments and populations rarely have perfectly constant growth rates.