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Rule of 72 Calculator

Estimate how long it takes for an investment to double with compound interest

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Investment
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How to Calculate the Rule of 72

The rule of 72 is a quick and easy calculation that helps someone estimate how long it takes for an investment, inflation, population, or really anything, to double with compounded growth. The completely accurate calculation involves natural logarithms which are not easy to calculate without a computer or spreadsheet, so this rule helps to estimate that calculation.

Rule of 72 Formula:

Time to Double = 72 ÷ Interest Rate

Exact Formula:

Time to Double = ln(2) ÷ ln(1 + r)

Where r is the interest rate as a decimal

Example

Suppose you have invested $1,000 in an account that pays 8.0% interest compounded annually. How long will it take for you to double your investment?

Using the Rule of 72: 72 ÷ 8 = 9 years (approximately)

Using the exact calculation: ln(2) ÷ ln(1.08) = 9.006 years

This means that your $1,000 investment will double to $2,000 in approximately 9 years, which is quite close to the completely accurate calculation.

Important Notes:

  • The Rule of 72 works best for interest rates between 6% and 10%
  • You can use different time periods (monthly, quarterly) by adjusting the rate accordingly
  • The rule can be applied to any exponential growth scenario, not just investments

Frequently Asked Questions (FAQ)

What is the Rule of 72?
The Rule of 72 is a quick mental calculation to estimate how long it takes for an investment to double at a given annual rate of return. You simply divide 72 by the interest rate to get the approximate number of years.
How accurate is the Rule of 72?
The Rule of 72 is quite accurate for interest rates between 6% and 10%. For rates outside this range, the approximation becomes less precise, but it still provides a useful quick estimate.
What is the exact formula for doubling time?
The exact formula is: Time = ln(2) / ln(1 + r), where r is the interest rate as a decimal. This gives the precise time needed for compound growth to double an investment.
Can I use this for other growth rates?
Yes! The Rule of 72 can be applied to any compound growth scenario, including population growth, inflation, or any exponentially growing quantity.
Is my data processed securely?
All calculations happen in your browser. No financial data is sent to any server, ensuring complete privacy and security.