72 法则计算器
本 72 法则计算器估算您的投资翻倍所需时间。只需将 72 除以年化收益率——在 8% 的收益率下，您的资金约 9 年翻倍。输入任意利率，查看精确的翻倍时间和复利增长预测。
Rule of 72 Calculator - Investment Doubling Time
The Rule of 72 Calculator helps you quickly estimate how long it will take for your investment to double in value. Simply enter either the annual rate of return or your target doubling time, and the Rule of 72 Calculator will automatically calculate the other value.
Frequently Asked Questions
72 法则是什么？
72 法则是估算投资翻倍所需时间的简便心算方法：翻倍年数 ≈ 72 / 年收益率(%)。例如，年收益率 8%：72/8 = 9 年资金翻倍。这是基于复利数学推导的近似公式，在 6-10% 的收益率范围内精度最高。
72 法则精确吗？
72 法则是近似公式，精确公式为翻倍年数 = ln(2) / ln(1+r) ≈ 0.693 / r。在 6-10% 利率范围内误差不超过 1%；在极低利率（< 2%）或极高利率（> 20%）时，使用 70 或 69 作为分子更精确。
72 法则有哪些应用场景？
72 法则不仅适用于投资回报计算，还可用于：估算债务翻倍时间（如信用卡年利率 18%，负债约 4 年翻倍）；通货膨胀对购买力的侵蚀（通胀率 3%，购买力约 24 年减半）；人口增长或任何以固定速率增长的量。
如何反向使用 72 法则？
可以反向计算：要在 N 年内翻倍，所需年收益率 ≈ 72/N。例如，希望 8 年内翻倍：需要年收益率约 72/8 = 9%。这帮助您设定合理的投资预期和评估不同投资机会是否能达成目标。
How to Calculate Investment Doubling Time Using Rule of 72
What is the Rule of 72?
The Rule of 72 is a simple mathematical concept that helps investors estimate how long it will take for an investment to double in value at a given annual rate of return. This rule of thumb provides a quick mental calculation for exponential growth scenarios.
Formula and Calculation
The Rule of 72 can be expressed in two ways:
- Years to Double = 72 ÷ Annual Rate of Return (%)
- Required Rate of Return (%) = 72 ÷ Years to Double
The Rule of 72 is most accurate for interest rates between 6% and 10%. Outside this range, the approximation becomes less precise.
Examples
Example 1: Finding Time to Double
With an 8% annual return: 72 ÷ 8 = 9 years to double the investment
Example 2: Finding Required Rate
To double in 6 years: 72 ÷ 6 = 12% annual return required
Limitations and Accuracy
While the Rule of 72 is a convenient approximation, it has some limitations:
- It's an approximation, not an exact calculation
- Most accurate for rates between 6% and 10%
- Assumes continuous compounding
- Doesn't account for taxes, fees, or other external factors
Rule of 72 Formula and Derivation
The Rule of 72 states: Years to Double = 72 ÷ Interest Rate.
This comes from the compound interest formula for doubling: 2 = (1 + r)^t, where r is the annual rate and t is the number of years.
Taking the natural logarithm: t = ln(2) / ln(1 + r)
For small rates, ln(1 + r) ≈ r, so t ≈ 0.693 / r. Multiplying both sides by 100 (to use percentage rates): t ≈ 69.3 / R.
The number 72 is used instead of 69.3 because:
- 72 is divisible by 2, 3, 4, 6, 8, 9, and 12, making mental math easier
- It provides a slight upward correction that improves accuracy at typical investment rates (6–10%)
Doubling Time Reference Table
| Annual Rate | Rule of 72 (years) | Exact (years) | Difference |
|---|---|---|---|
| 1% | 72.0 | 69.7 | +2.3 |
| 2% | 36.0 | 35.0 | +1.0 |
| 3% | 24.0 | 23.4 | +0.6 |
| 4% | 18.0 | 17.7 | +0.3 |
| 5% | 14.4 | 14.2 | +0.2 |
| 6% | 12.0 | 11.9 | +0.1 |
| 7% | 10.3 | 10.2 | +0.1 |
| 8% | 9.0 | 9.0 | 0.0 |
| 9% | 8.0 | 8.0 | 0.0 |
| 10% | 7.2 | 7.3 | -0.1 |
| 12% | 6.0 | 6.1 | -0.1 |
| 15% | 4.8 | 5.0 | -0.2 |
| 20% | 3.6 | 3.8 | -0.2 |
Rule of 72 vs Rule of 69 vs Rule of 70
Three related rules exist for estimating doubling time:
- Rule of 69.3: Most mathematically accurate (based on ln(2) = 0.693). Best for continuous compounding and very low rates (below 4%).
- Rule of 70: A compromise between accuracy and mental math convenience. Common in economics and demographics for estimating GDP or population doubling time.
- Rule of 72: Best for annual compounding at typical investment rates (6–10%). Preferred in finance because 72 has more divisors, making mental division easier.
| Growth Rate | Rule of 69 | Rule of 70 | Rule of 72 | Exact |
|---|---|---|---|---|
| 2% | 34.7 | 35.0 | 36.0 | 35.0 |
| 5% | 13.9 | 14.0 | 14.4 | 14.2 |
| 8% | 8.7 | 8.8 | 9.0 | 9.0 |
| 10% | 6.9 | 7.0 | 7.2 | 7.3 |
| 15% | 4.6 | 4.7 | 4.8 | 5.0 |