The Rule of 72 is a mental math shortcut for estimating how long it takes an investment to double. Divide 72 by the annual return and the result is approximately the number of years needed: at 6% returns, money doubles in 12 years; at 9%, it doubles in 8 years; at 12%, in 6 years.
The Rule of 72 Formula
$$\text{Years to Double} = \frac{72}{\text{Annual Rate of Return (%)}}$$
That’s the entire formula. No calculator required.
Doubling Time by Rate of Return
| Annual Return | Years to Double (Rule of 72) | Exact Doubling Time |
|---|---|---|
| 1% | 72 years | 69.7 years |
| 2% | 36 years | 35.0 years |
| 3% | 24 years | 23.4 years |
| 4% | 18 years | 17.7 years |
| 5% | 14.4 years | 14.2 years |
| 6% | 12 years | 11.9 years |
| 7% | 10.3 years | 10.2 years |
| 8% | 9 years | 9.0 years |
| 9% | 8 years | 8.0 years |
| 10% | 7.2 years | 7.3 years |
| 12% | 6 years | 6.1 years |
| 15% | 4.8 years | 4.96 years |
| 24% | 3 years | 3.22 years |
The Rule of 72 is most accurate between 6%–10%. At very low or very high rates it slightly overestimates doubling time.
Real-World Examples
Example 1: Stock Market Investment
The S&P 500 has returned approximately 10% annually (before inflation) over the long run.
- Rule of 72: 72 ÷ 10 = 7.2 years to double
- $10,000 invested today → ~$20,000 in 7.2 years → ~$40,000 in 14.4 years → ~$80,000 in 21.6 years
| Start | 7.2 Years | 14.4 Years | 21.6 Years | 28.8 Years |
|---|---|---|---|---|
| $10,000 | $20,000 | $40,000 | $80,000 | $160,000 |
| $25,000 | $50,000 | $100,000 | $200,000 | $400,000 |
| $50,000 | $100,000 | $200,000 | $400,000 | $800,000 |
Example 2: High-Yield Savings Account at 4.5% APY
- Rule of 72: 72 ÷ 4.5 = 16 years to double
- Good for capital preservation; not a wealth-building vehicle at this rate
Example 3: 401(k) at 7% Average Return
- Rule of 72: 72 ÷ 7 = ~10.3 years to double
- A 30-year-old with $50,000 in their 401(k): $100,000 at 40, $200,000 at 50, $400,000 at 60
Example 4: Credit Card Debt at 24% Interest
- Rule of 72: 72 ÷ 24 = 3 years to double
- $5,000 unpaid credit card balance → $10,000 in 3 years → $20,000 in 6 years
This is why high-interest debt destroys wealth — the same compounding that grows investments destroys finances when applied to unpaid balances.
Rule of 72 for Inflation
The Rule of 72 also shows how inflation erodes purchasing power:
| Inflation Rate | Years Until Prices Double | Purchasing Power Halves |
|---|---|---|
| 2% | 36 years | By 2062 |
| 3% | 24 years | By 2050 |
| 4% | 18 years | By 2044 |
| 7% | ~10 years | By 2036 |
At 3% inflation (near the 2026 Fed target zone), a $1,000 monthly expense becomes $2,000 in today’s dollars by 2050. This is the core argument for investing — cash under a mattress loses half its purchasing power in 24 years.
Rule of 72 for Debt Payoff
Use the Rule of 72 in reverse: if you want to understand how quickly debt grows without payments, divide 72 by the interest rate.
| Loan Type | Typical Rate | Debt Doubles In |
|---|---|---|
| Credit card | 20%–29% | 2.5–3.6 years |
| Personal loan | 10%–20% | 3.6–7.2 years |
| Student loan | 5%–8% | 9–14 years |
| Mortgage | 6%–7% | 10–12 years |
| Auto loan | 5%–10% | 7.2–14 years |
Why the Rule of 72 Uses 72
Mathematically, the exact doubling formula is:
$$\text{Exact doubling time} = \frac{\ln(2)}{\ln(1 + r)} \approx \frac{0.693}{r}$$
This gives the Rule of 69.3 as the mathematically exact form. The number 72 is used instead because:
- It is close to 69.3 but slightly more accurate at 6%–10% returns (the most common investment rates)
- 72 has many integer divisors: 1, 2, 3, 4, 6, 8, 9, 12 — making mental division easy for common rates like 4%, 6%, 8%, 9%, and 12%
Rule of 72 vs Rule of 70 vs Rule of 69.3
| Rule | Divide By | Best For |
|---|---|---|
| Rule of 72 | 72 | Easy mental math; accurate at 6%–10% |
| Rule of 70 | 70 | Low interest rates (1%–5%); more precise there |
| Rule of 69.3 | 69.3 | Continuous compounding; most mathematically exact |
For practical financial planning, use Rule of 72. It divides more cleanly and is accurate enough for any investment decision.
The rule of 72 quantifies the power of compounding — see best long-term investments for the investment types that historically achieve the highest compounding rates. Investment fees reduce your effective return rate — see cost of investment fees over time to calculate how even 1% extra in annual fees changes your doubling time. For practical investment strategies that maximize compounding, see investment strategies.
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