Rule of 72

Extracted Attributes

• Field

  Finance, Mathematics

• Formula

  72 / annual interest rate (%) = number of years to double

• Purpose

  Estimates the time for an investment to double in value, or for a quantity to halve (decay), based on a fixed annual rate of return.

• Application

  Exponential growth (compound interest), financial planning, debt management, inflation, GDP growth

• Adaptability

  Can be adapted to estimate tripling times or the time it takes for an investment to grow by a specific percentage.

• Accuracy Range

  Most accurate for interest rates between 6% and 10%

• Alternative Numbers

  Rule of 70, Rule of 69.3 (more accurate for continuous compounding)

Rule of 72

In finance, the rule of 72, the rule of 70 and the rule of 69.3 are methods for estimating an investment's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period (usually years) to obtain the approximate number of periods required for doubling. Although scientific calculators and spreadsheet programs have functions to find the accurate doubling time, the rules are useful for mental calculations and when only a basic calculator is available. These rules apply to exponential growth and are therefore used for compound interest as opposed to simple interest calculations. They can also be used for decay to obtain a halving time. The choice of number is mostly a matter of preference: 69 is more accurate for continuous compounding, while 72 works well in common interest situations and is more easily divisible. There are a number of variations to the rules that improve accuracy. For periodic compounding, the exact doubling time for an interest rate of r percent per period is t = ln ⁡ ( 2 ) ln ⁡ ( 1 + r / 100 ) ≈ 72 r {\displaystyle t={\frac {\ln(2)}{\ln(1+r/100)}}\approx {\frac {72}{r}}} , where t is the number of periods required. The formula above can be used for more than calculating the doubling time. If one wants to know the tripling time, for example, replace the constant 2 in the numerator with 3. As another example, if one wants to know the number of periods it takes for the initial value to rise by 50%, replace the constant 2 with 1.5.

Web Search Results

• The Rule of 72: Definition, Usefulness, and How to Use It

  The Rule of 72 is a simplified formula that calculates how long it’ll take for an investment to double in value, based on its rate of return. The Rule of 72 applies to compounded interest rates and is reasonably accurate for interest rates that fall in the range of 6% and 10%. The Rule of 72 can be applied to anything that increases exponentially, such as GDP or inflation; it can also indicate the long-term effect of annual fees on an investment’s growth. [...] Here’s how the Rule of 72 works. You take the number 72 and divide it by the investment’s projected annual return. The result is the number of years, approximately, it’ll take for your money to double. [...] The Rule of 72 primarily works with interest rates or rates of return that fall in the range of 6% and 10%. When dealing with rates outside this range, the rule can be adjusted by adding or subtracting 1 from 72 for every 3 points the interest rate diverges from the 8% threshold.

• The Rule of 72: What It Is and How to Use It in Investing - Investopedia

  The Rule of 72 is a quick and easy method for determining how long it will take to double the money you're investing, assuming it has a fixed annual rate of return. While it is not precise, it does provide a ballpark figure and is easy to calculate. [...] The Rule of 72 is an easy way to calculate how long an investment will take to double in value given a fixed annual rate of interest. Dividing 72 by the annual rate of return gives investors an estimate of how many years it will take for the initial investment to duplicate. It is a reasonably accurate estimate, especially at low interest rates. For a more accurate estimate, taking compound interest into account, you can use the rule of 69.3%. ### Key Takeaways [...] The Rule of 72 is a quick way to get a useful ballpark figure. For investments without a fixed rate of return, you can instead divide 72 by the number of years you hope it will take to double your money. This will give you an estimate of the annual rate of return you’ll need to achieve that goal. The calculation is most accurate for rates of return of about 5% to 10%.

• The Rule of 72: What is it and how does it work? - Saxo Bank

  The Rule of 72 is a valuable tool for estimating how investments, inflation, or debt evolve over time. Its simplicity and versatility make it a practical resource for evaluating growth potential and setting realistic financial goals. By using it, you can gain a clearer perspective on the impact of returns and financial variables, helping you align your strategies with your long-term objectives. [...] The Rule of 72 in investing is built on the principle of compounding, where returns are calculated not just on the initial investment but also on the accumulated gains over time. It provides a quick estimate of either the time required to double an investment, or the annual rate of return needed to achieve that goal.

• How the Rule of 72 Can Help You Build Wealth—Or Sink Deeper ...

  The Rule of 72 is a quick formula that estimates how long it takes for money to double, whether it's an investment or a debt. The calculation is simple: 72 ÷ annual interest rate (%) = number of years for money to double. This formula works for savings and debt, showing how compound interest can either grow your wealth or magnify your financial obligations. Image 6) Delete Edit embedded media in the Files Tab and re-insert as needed. align image leftalign image centeralign image right [...] ### 3. Set Financial Goals: Use the Rule of 72 to estimate how long it will take to double your savings for goals like studying abroad, buying a car, or starting a business. Stay proactive about managing debt to keep financial goals on track. Final Thoughts -------------- The Rule of 72 is a simple yet powerful tool that makes complex financial concepts easier to understand. Whether you’re saving for the future or managing debt, applying this rule can help you: [...] Whether you are saving for a goal or dealing with debt, the Rule of 72 offers a simple, yet effective way to estimate the time it takes for money to grow or for debt to balloon due to compound interest.

• Rule of 72 - Wikipedia

  In finance, the rule of 72, the rule of 70( and the rule of 69.3 are methods for estimating an investment's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period (usually years) to obtain the approximate number of periods required for doubling. Although scientific calculators and spreadsheet programs have functions to find the accurate doubling time, the rules are useful for mental calculations and when only a basic calculator is available.( [...] For instance, if you were to invest $100 with compounding interest at a rate of 9% per annum, the rule of 72 gives 72/9 = 8 years required for the investment to be worth $200; an exact calculation gives ln(2)/ln(1+0.09) = 8.0432 years. Similarly, to determine the time it takes for the value of money to halve at a given rate, divide the rule quantity by that rate.

In finance, the rule of 72, the rule of 70 and the rule of 69.3 are methods for estimating an investment's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period (usually years) to obtain the approximate number of periods required for doubling. Although scientific calculators and spreadsheet programs have functions to find the accurate doubling time, the rules are useful for mental calculations and when only a basic calculator is available. These rules apply to exponential growth and are therefore used for compound interest as opposed to simple interest calculations. They can also be used for decay to obtain a halving time. The choice of number is mostly a matter of preference: 69 is more accurate for continuous compounding, while 72 works well in common interest situations and is more easily divisible.There are a number of variations to the rules that improve accuracy. For periodic compounding, the exact doubling time for an interest rate of r percent per period is , where t is the number of periods required. The formula above can be used for more than calculating the doubling time. If one wants to know the tripling time, for example, replace the constant 2 in the numerator with 3. As another example, if one wants to know the number of periods it takes for the initial value to rise by 50%, replace the constant 2 with 1.5.