Use the Rule of 72 to estimate how long it takes to double your money at a given annual return rate — and find the rate needed to double by a target date.
The Rule of 72 is a quick mental math shortcut for estimating how long compound
interest takes to double an investment.
Formula
Doubling time (years) ≈ 72 ÷ Annual Rate (%)
Required rate ≈ 72 ÷ Target years
Why 72?
72 is divisible by 1, 2, 3, 4, 6, 8, 9, 12, and 24 — making mental math easy.
The exact formula uses ln(2) ÷ ln(1 + r), but 72/r is accurate to within 1–2%
for rates between 2–20%.
Doubling time by rate
Annual rate
Doubling time
2%
36 years
4%
18 years
6%
12 years
8%
9 years
10%
7.2 years
12%
6 years
24%
3 years
72%
1 year
The Rule of 72 and inflation
Inflation uses the rule too. At 3% inflation, purchasing power halves in 24 years.
This is why earning above inflation is essential for real wealth preservation.
Exponential growth applications
The Rule of 72 works for any exponential process:
- SaaS ARR growth rate → years to double revenue
- Population growth → doubling time
- Debt at given interest rate → years to double what you owe
Explanation of the Rule of 72 with examples: how to estimate doubling time for investments, debt, and revenue growth using simple mental math.
The Rule of 72 is a mental math shortcut: divide 72 by an annual rate
to estimate how many years it takes for a quantity to double.
Examples
Investment at 8% annual return: 72 ÷ 8 = 9 years to double
Credit card at 24% APR: 72 ÷ 24 = 3 years for debt to double
Inflation at 3%: 72 ÷ 3 = 24 years for prices to double
SaaS growing 50% YoY: 72 ÷ 50 = ~1.4 years to double ARR
Why does it work?
At rate r, the exact doubling time is ln(2) ÷ ln(1 + r).
For small rates, this approximates to 0.693 / r.
The Rule of 72 uses 72 instead of 69.3 because 72 is more
divisible by common interest rates (2, 3, 4, 6, 8, 9, 12...).
Accuracy
The Rule of 72 is most accurate between 6–10% rates (< 1% error).
For rates above 20%, use the Rule of 72 calculator
which shows both the approximation and exact doubling time.
Compare the Rule of 72 approximation with the exact compound interest doubling time. When to use each and how much error the shortcut introduces.
The two formulas
Rule of 72: Years ≈ 72 / annual rate
Exact formula: Years = ln(2) / ln(1 + r) where r = rate as decimal
Error comparison
Rate
Rule of 72
Exact
Error
2%
36 yrs
35.0 yrs
+2.9%
4%
18 yrs
17.7 yrs
+1.7%
8%
9 yrs
9.0 yrs
0.0%
12%
6 yrs
6.1 yrs
−1.4%
20%
3.6 yrs
3.8 yrs
−4.5%
50%
1.44 yrs
1.71 yrs
−16%
For most practical financial decisions at rates under 20%, the Rule of 72
is close enough. For rates above 20% (high-growth companies, high-interest
debt), use the exact formula.
The Rule of 72 calculator shows both
values side by side so you can see the difference for any rate.