When it comes to understanding how long it takes for an investment or a population to double, the Rule of 70 and the Rule of 72 are invaluable tools. These rules provide quick estimates for doubling times based on growth rates, making them popular among investors and demographers alike. But when should you use each rule, and how do they differ?
What is the Rule of 70?
The Rule of 70 is a simple formula used to estimate the number of years it will take for a quantity to double, given a fixed annual growth rate. To use the Rule of 70, divide 70 by the annual growth rate (expressed as a percentage). This rule is particularly useful for calculating the doubling time of populations or investments with lower growth rates.
How to Apply the Rule of 70?
To apply the Rule of 70, follow these steps:
- Identify the annual growth rate of the quantity you are examining.
- Divide 70 by this growth rate to find the doubling time.
Example: If a population is growing at a rate of 2% per year, the doubling time is:
[ \text{Doubling Time} = \frac{70}{2} = 35 \text{ years} ]
What is the Rule of 72?
The Rule of 72 is another quick calculation method to estimate the doubling time of an investment or population. Like the Rule of 70, it involves dividing a constant by the annual growth rate. However, the Rule of 72 is often preferred for financial calculations, especially when dealing with interest rates and returns on investment.
How to Apply the Rule of 72?
To use the Rule of 72 effectively:
- Determine the annual growth rate or interest rate.
- Divide 72 by this rate to estimate the doubling time.
Example: For an investment growing at an annual interest rate of 6%, the doubling time is:
[ \text{Doubling Time} = \frac{72}{6} = 12 \text{ years} ]
When to Use the Rule of 70 vs. 72?
Choosing between the Rule of 70 and the Rule of 72 depends on the context and the growth rate involved. Here’s a quick guide:
- Use the Rule of 70 for lower growth rates (typically below 5%). It provides more accurate estimates for demographic changes and slower-growing investments.
- Use the Rule of 72 for higher growth rates and financial calculations. It is often more accurate for investments with interest rates between 6% and 10%.
Why Do These Rules Work?
Both rules are derived from the mathematical concept of logarithms, specifically the natural logarithm of 2 (approximately 0.693). The constant 70 or 72 is chosen based on empirical observations that make the calculations simple and reasonably accurate for most practical purposes.
Practical Examples
Population Growth
Consider a city with a population growth rate of 1.5% per year. Using the Rule of 70:
[ \text{Doubling Time} = \frac{70}{1.5} \approx 46.7 \text{ years} ]
This means the city’s population will double in about 47 years.
Investment Growth
For a mutual fund with an annual return of 8%, the Rule of 72 provides:
[ \text{Doubling Time} = \frac{72}{8} = 9 \text{ years} ]
Thus, the investment will double in approximately 9 years.
Comparison Table: Rule of 70 vs. Rule of 72
| Feature | Rule of 70 | Rule of 72 |
|---|---|---|
| Best For | Low growth rates | Financial calculations |
| Typical Use | Population growth | Investment growth |
| Accuracy Range | Below 5% growth | 6% to 10% growth |
| Calculation | 70 / growth rate | 72 / growth rate |
People Also Ask
What is a good growth rate for using the Rule of 70?
The Rule of 70 is most accurate for growth rates below 5%. It is widely used in demographics and economics to estimate doubling times for populations and slow-growing investments.
How accurate are the Rules of 70 and 72?
Both rules provide rough estimates rather than precise calculations. They are accurate enough for quick assessments but should be supplemented with more detailed analyses for critical financial decisions.
Can the Rule of 72 be used for non-financial growth?
Yes, the Rule of 72 can be applied to any scenario involving exponential growth, though it is most commonly used for financial purposes. For non-financial growth, the Rule of 70 might be more appropriate, especially for lower growth rates.
Why is the Rule of 72 preferred in finance?
The Rule of 72 is preferred in finance due to its simplicity and reasonable accuracy for a wide range of interest rates. It allows investors to quickly estimate how long it will take for their investments to double, aiding in financial planning and decision-making.
Are there other rules similar to 70 and 72?
Yes, there are variations like the Rule of 69 and the Rule of 69.3, which are based on more precise mathematical calculations involving continuous compounding. However, these are less commonly used due to their complexity.
Conclusion
Understanding when to use the Rule of 70 or Rule of 72 can significantly enhance your ability to make informed decisions about investments and demographics. By selecting the appropriate rule based on growth rates and context, you can quickly estimate doubling times and plan accordingly. For more detailed financial planning, consider consulting a financial advisor or using advanced financial modeling tools.
