Years to Double (Rule of 72): 0.00
Exact Years to Double: 0.00
Doubled Amount: $0.00
Final Amount: $0.00
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Rule of 72 calculator: A highly advanced financial planner that calculates in just seconds the time it will take an investment to double in value via compound interest. This math-quick-fix makes sense for long-term investments, retirement plans, and even inflation-related purchasing power. This is just an estimate, but the Rule of 72 gives you remarkably close estimates for 6% to 10% interest rates.
The Rule of 72 is perhaps the most beautiful and practical principle in finance mathematics. Divide 72 by the rate of return every year, and the investors know quickly how many years it will take for an investment to double in value. This is an effective measure of the power of compound interest, and can be used in many different financial applications, from asset appreciation to inflationary effects.
The basic formula is straightforward: Years to Double = 72 ÷ Annual Rate of Return
For example:
The Rule of 72 comes from the sophisticated mathematical equation for compound interest and natural logarithms. The real equation for how long it takes to double a investment is:
T = ln(2) ÷ ln(1 + r)
Where:
The number 72 was picked as it’s smaller than a lot of smaller numbers (2, 3, 4, 6, 8, 9, and 12), so it’s more efficient in mind-work. The mathematical constant is actually a bit less than 69.3 for ongoing compounding, but 72 is better for most actual situations of annual compounding.
More precise for the ongoing compounding case (especially academic/theoretical use cases). This is the rule with the best mathematical precision but not as much usable in the head.
Frequently applied to calculate the inflation impact or the growth of GDP. This range is a good compromise between precision and ease of use especially with 5%-10% rates.
Improves precision for high interest rates (greater than 10%). In terms of returns between 15-20% this adjustment is more than sufficient to absorb the compounding effect.
The Rule of 72 allows investors to grasp the time-return relation so they can:
In terms of retirement planning, the Rule of 72 tells us a lot about:
The principle can also show how fees have an effect on the growth of investments:
The Rule of 72 is an excellent piece of advice, and you should be mindful of its limits:
The maxim applies best to a rate of interest of between 6% and 10%. For rates beyond this range, use modified rules:
The rule makes several important assumptions: