Rule of 72
"Divide 72 by the growth rate to find how long it takes to double"
Origin: Finance & Banking
The Key Insight
The Rule of 72 is accurate math applied to a false premise. The doubling calculation is correct; the assumption that exponential growth continues is not.
What People Think
A convenient mental math trick for compound interest calculations. Want to know when your investment doubles at 8%? 72 / 8 = 9 years.
The Deeper Truth
This is a specific case of exponential growth dynamics. The actual formula is ln(2)/r (approximately 0.693/r), rounded to 72/r for easy mental math. But here's what most people miss: biology shows that exponential growth is always a temporary phase. Every population, every company, every market eventually hits resource constraints and transitions to logistic (S-curve) growth.
Biological Parallel
Bacterial populations double at predictable intervals under ideal conditions - E. coli every 20 minutes. But no bacterial colony grows exponentially forever. They hit nutrient limits, waste accumulation, or space constraints. The same math governs tumor growth, viral spread, and population dynamics. The doubling time is real; the assumption it continues indefinitely is the error.
Business Application
Used for compound interest, revenue growth projections, market sizing, and viral coefficient calculations. Useful for early-stage projections but dangerous when extrapolated. A company growing at 50% annually doesn't actually double every 1.4 years forever - market saturation, competition, and operational complexity eventually flatten the curve.
When It Breaks Down
The rule assumes sustained exponential growth, which biology proves is impossible long-term. It fails during market saturation, resource constraints, competitive pressure, or when the denominator (growth rate) changes. The real question isn't 'when do I double?' but 'when does my growth rate start declining?'