Calculate Doubling Time
What Is the Rule of 72?
The Rule of 72 is a simple mental math shortcut: divide 72 by your annual interest rate to estimate how many years it takes to double your money. At 8% interest, 72 ÷ 8 = 9 years. The actual mathematical result is about 9.01 years — remarkably close.
Why 72 Works
The number 72 is chosen because it has many divisors and approximates the natural logarithm calculation well for typical interest rates (between 6% and 10%). For very high or very low rates, the approximation drifts slightly from the exact answer.
Real-World Examples
- High-yield savings (4%): 18 years to double
- Stock market average (10%): 7.2 years to double
- Credit card debt (20%): 3.6 years for the bank to double THEIR money on YOU
The Power of Multiple Doublings
If your money doubles every 7 years and you invest for 35 years, that is 5 doublings. $10,000 becomes $20,000, then $40,000, $80,000, $160,000, and finally $320,000. This is why starting early matters so much.
Rule of 72 for Inflation
You can also use the Rule of 72 to see how quickly inflation erodes purchasing power. At 3% inflation, prices double in about 24 years (72 ÷ 3). This is why simply keeping cash under your mattress loses value over time.
Frequently Asked Questions
How accurate is the Rule of 72? +
The Rule of 72 is most accurate for interest rates between 6% and 10%. At 8%, it is off by less than 0.1 years. At very high rates (above 20%) or very low rates (below 4%), the approximation becomes less precise. For exact calculations, use the formula: ln(2) / ln(1 + r).
Can I use the Rule of 72 for monthly compounding? +
Yes, but use the effective annual rate rather than the nominal rate. If your account compounds monthly at 8% APR, the effective annual rate is slightly higher (about 8.3%), so the doubling time is slightly shorter than 9 years.
Does the Rule of 72 work for halving too? +
Yes. You can use it to estimate how long it takes for inflation to cut your purchasing power in half, or how long it takes for a population to halve at a given decline rate. The math works the same way in reverse.