**This rule 72 calculator is based on the Rule of 72, a mathematical shortcut to provide a quick accurate approximation for investment growth over time.**

The calculation of **Rule of 72 **helps **investors **and **financial planners** estimate how long it will take for an investment to **double in value**, given a fixed annual rate of return.

## Rule of 72 Calculator

Interest Rate | Years to Double |
---|---|

2% | 36 years |

4% | 18 years |

6% | 12 years |

8% | 9 years |

10% | 7.2 years |

12% | 6 years |

## Rule of 72 Calculation Formula

The formula for the Rule of 72 is remarkably simple:

**Years to double = 72 / Annual rate of return**

For example, if you have an investment with an **annual return of 8%**, the calculation would be:

**72 / 8 = 9 years**

This means that at an 8% annual return, your investment would take **approximately 9 years to double** in value.

## What is the Rule of 72?

The Rule of 72 is a **mathematical concept** used in finance to provide a quick estimate of how long it will take for an investment to double, given a fixed annual rate of return.

This rule is a **simplified way to perform exponential growth calculations** in your head, making it a valuable tool for investors, financial advisors, and anyone interested in understanding the potential growth of their money over time.

The Rule of 72 is based on the concept of **compound interest**, where interest is earned not only on the principal amount but also on the accumulated interest from previous periods.

This **compounding effect** can lead to significant growth over time, and the Rule of 72 helps to illustrate this power in a simple, easy-to-understand way.

While the Rule of 72 is **not exact**, it provides a **reasonably accurate approximation** for most practical purposes, especially for annual return rates between 6% and 10%.

## How Does the Rule of 72 Work?

The Rule of 72 works by leveraging a **mathematical relationship** between the doubling time of an investment and its growth rate. Here’s how it functions in practice:

**Estimate doubling time**: By dividing 72 by the annual rate of return, you get an approximation of how many years it will take for your investment to double.**Inverse calculation**: You can also use the rule to determine what interest rate you need to double your money in a specific number of years. Simply divide 72 by the desired number of years.**Comparison tool**: The Rule of 72 allows for quick comparisons between different investment options or scenarios.**Inflation consideration**: The rule can also be applied to understand the effects of inflation on purchasing power over time.

Let’s look at some examples to illustrate how the Rule of 72 works in practice:

- If you have an investment earning
**6% annually**, it will take approximately**12 years to double**(72 / 6 = 12). - To double your money in
**10 years**, you would need an annual return of about**7.2%**(72 / 10 = 7.2). - If inflation is at
**3% per year**, the purchasing power of your money will halve in about**24 years**(72 / 3 = 24).

## How long will it take $1000 to double at 6% interest?

Using the Rule of 72, we can calculate:

**72 / 6 = 12 years**

It will take **approximately 12 years** for $1000 to double to $2000 at a 6% interest rate.

## Does the Rule of 72 really work?

The Rule of 72 is an **approximation**, but it works remarkably well for most practical purposes. It’s particularly accurate for interest rates between **6% and 10%**. For rates outside this range, it becomes less precise but still provides a useful estimate.

To demonstrate its accuracy, let’s compare it with the exact calculation for doubling time:

**Exact formula**: T = ln(2) / ln(1 + r), where T is time and r is the interest rate as a decimal.

For 6% interest:

- Rule of 72: 72 / 6 = 12 years
- Exact calculation: ln(2) / ln(1.06) ≈ 11.90 years

As you can see, the Rule of 72 gives a result that’s very close to the exact calculation, off by only about 0.1 years in this case.

## How many years to double money at 7 percent?

Using the Rule of 72:

**72 / 7 = 10.29 years**

Therefore, it will take **approximately 10.29 years** for money to double at a 7% interest rate.

For comparison, the exact calculation gives: ln(2) / ln(1.07) ≈ 10.24 years

Again, we see that the Rule of 72 provides a very close approximation to the exact value.