The doubling rule of 69, often referred to simply as the Rule of 69, is a mathematical formula used to estimate the time it takes for an investment or an amount to double in value, given a fixed annual interest rate that is compounded continuously. It's particularly useful for quickly estimating the growth of investments, loans, or even populations.
Understanding the Rule of 69
While the more commonly known Rule of 72 provides a quick estimate for compounding interest, the Rule of 69 offers a slightly more accurate approximation, especially when dealing with interest that is compounded continuously. It provides a simple way to gauge how long it will take for your money to grow.
The Formula
The basic formula for the Rule of 69 is:
Doubling Time (in years) = 69 / Annual Rate of Return (as a percentage)
However, for enhanced accuracy, especially in scenarios like real estate investing where continuous compounding is a closer approximation, a refined version of the rule incorporates an adjustment:
Doubling Time (in years) = (69 / Annual Rate of Return as a percentage) + 0.35
This adjustment helps to refine the estimate further, making it more precise for certain financial calculations.
Practical Application and Examples
Let's illustrate the Rule of 69 with a practical example, as seen in real estate investment:
Example: A real estate investor is earning a twenty percent (20%) annual return on their investment.
Using the refined Rule of 69 formula:
- Divide 69 by the annual rate of return: 69 / 20 = 3.45
- Add 0.35 to the result: 3.45 + 0.35 = 3.8
Therefore, according to the Rule of 69, it would take approximately 3.8 years for the investor's money to double at a 20% continuous annual return.
Why is it Useful?
- Quick Estimation: It allows investors and financial planners to make rapid mental calculations without needing a calculator or complex formulas.
- Financial Planning: It helps in setting realistic expectations for investment growth and long-term financial goals.
- Comparative Analysis: Investors can use it to compare different investment opportunities based on their potential doubling times.
Rule of 69 vs. Rule of 72
Both rules serve a similar purpose but are best suited for different scenarios:
Feature | Rule of 69 | Rule of 72 |
---|---|---|
Primary Use | More accurate for continuous compounding | General use for annually compounded interest |
Formula | (69 / Rate) + 0.35 (for more accuracy) | 72 / Rate |
Accuracy | Higher accuracy for continuous compounding | Good approximation for most annual compounding |
Best For | Highly liquid investments, continuous growth | Stocks, bonds, savings accounts |
The Rule of 69 provides a slight edge in accuracy for situations where interest is compounded very frequently, or continuously.