# Rule of 72 Calculator

### What You Should Know

- The Rule of 72 allows you to estimate how long it will take for an investment to double given an interest rate.
- You can also use this rule to calculate the rate of return your investment requires to double in a certain timeframe.
- There are different variations of the Rule of 72. There is a Rule of 69 and the Rule of 70 that have the same purpose but provide more precise results.
- This calculator allows you to estimate the timeframe for an investment to double as well as the interest rate required for all three rules.

#### Calculator for

## About This Calculator

This simple calculator allows you to estimate the interest rate required to double your money within a specified time frame. It also allows you to calculate the number of years it will take to double your money at a specified annual interest rate. This calculator can use three similar rules including the rule of 72, the rule of 70, and the rule of 69. All of these rules calculate a similar value, but they yield results with different accuracy.

Rule 69 tends to be the most accurate among all other rules. The rule of 70 is more accurate for negative returns and positive returns of up to 4%. Lastly, the rule of 72 is more accurate for positive returns from 6% to 10%.

You can input the number of years, months, or days required to double your money, and it will calculate the interest rate required for that. You can also input the interest rate to calculate the doubling time for the specific interest rate.

## What Is a Rule of 72?

This is a rule of thumb that allows an individual to estimate the number of years for their investment to double. It can also be used to calculate the compounded interest rate given the number of years required for an investment to double. A Rule of 72 is derived using the formula for exponential growth, so it assumes a compounding interest as opposed to a simple interest. The following assumptions are required for the Rule of 72 to work:

- Constant compounding rate over time.
- This rule assumes exponential growth.
- Accurate for interest rates that fall between 6% and 10%.

Usually, scientific calculators as well as Excel spreadsheets have built-in formulas that calculate the interest rate more precisely than the 72 Rule. On the other hand, the Rule of 72 is a simple way to estimate the doubling time required for an investment at a given interest rate. This rule is useful for the mental calculation of a compounding interest rate.

### Rule of 72 Example

An individual is considering adding a well-diversified mutual fund to their retirement portfolio that should grow exponentially in the long term. The individual estimates that they want to see their portfolio value double every 14 years, and they would like to know what interest rate they would require to achieve this objective. They perform the following calculation:

Required Rate of Return = 72 / 14 Years = 5.14%.

The individual finds out that their investment requires a 5.14% return. The individual also notes that the current rate of return of the investment portfolio is 7%, and they want to calculate how many years it takes for their portfolio to double in value. They perform the following calculation:

Number of Years = 72 / 7% = 10.29 Years.

To use a Rule of 72, an individual simply needs to divide 72 by the interest rate. It is important to know how it is derived to understand why the formula works. The following section explains how the Rule of 72 is derived.

### Rule of 72 Formula

This rule is derived from the Time Value of Money (TVM) formula:

The Rule of 72 estimates how many years it takes for an investment to double in value at a given Rate of Return. Since we are looking for the Number of Years when the Future Value = 2 x Present Value, we need to solve the following equation:

When Rate of Return is small, the formula for the Number of Years equals to the following:

The most precise way to estimate the number of years it takes for an investment to double is to divide 69.3 by the Rate of Return. There is even a Rule of 69 that exists to capture this relationship. The Rule of 72 uses the same logic, but it uses the number 72 because it is easier to work with. In addition to the two rules mentioned above, there is a Rule of 70 that has the same purpose as the other two rules.

## Alternative Rules

There are two alternatives to the Rule of 72 that may not be as popular because it is more difficult to do mental math with them, but they tend to yield more precise results. Both rules have similar assumptions, and they generally work similarly.

All of these rules are used to either calculate the number of years it takes for an investment to double or the rate of return on the investment required for it to double at a given timeframe. The rules require the return on the investment to be constant over time, but an average return may also be a good approximation. These rules may be useful for bond, stock, and real estate investing.

### Rule of 70

Similar to a Rule of 72, the Rule of 70 allows individuals to estimate the rate of return required to double their investment in a set timeframe. It is important to note that 70 is more accurate for negative returns up to +4%, while 72 is more accurate for over +6% returns. The rule of 70 calculates the interest rate and the years to double the investment more precisely than the Rule of 72. On the other hand, it may be more difficult to conduct mental calculations using the Rule of 70. The following formulas are used to do necessary calculations with the Rule of 70.

#### Rule of 70 Formula Set

To Calculate Number of Years | To Calculate Rate of Return |
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### Rule of 69

This rule may yield even more precise results than the Rule 70 and the Rule 72. The Rule 69 may be one of the best to use when an individual is estimating how long it takes for an investment to double at a continuous compounding of a fixed rate of return. Just as the other two rules, the Rule of 69 can also estimate the interest rate it takes for an investment to double at a given timeframe. The following formulas are related to this rule.

#### Rule of 69 Formula Set

To Calculate Number of Years | To Calculate Rate of Return |
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