# Rule of 72

Rule of 72 uses the amount of time an investment takes to double in value at a fixed annual rate of return) You can use this simple formula to find out how long it will take your money to double while you sit back and relax.

## What Is the Rule of 72?

Using the rule of 72, one can calculate the number of years required to double an investment at a given rate of return. It can also calculate the annual rate of compounded return from an investment based on how long it will take to double the investment.

Although calculators and spreadsheet programs such as Microsoft Excel have functions to precisely calculate the time it will take to double the invested money, the rule of 72 comes in handy for mental calculations to quickly get an estimate. As a result, the rule of 72 is often taught to beginning investors because it is easy to understand and calculate. The Securities and Exchange Commission also refers to the rule of 72 on a grade-level basis in its financial literacy materials

## When will an investment double (in years)?

The rule of 72 estimates how long it will take for an investment to double.

This can be a fairly accurate measurement, especially when using lower interest rates rather than higher ones. This method is used when compound interest is involved. The rule of 72 does not work very well with simple interest rates.

The following table shows the difference between the rule of 72 calculation and the actual number of years an investment needs to double in value:

## Rule of 72 Formula

Here is the rule of 72 formula:

## Example of the Rule of 72

You own a company that manufactures coffee machines. In order to finance the construction of a factory and warehouse for coffee machines, you have turned to private investors. John, a high-net-worth individual willing to contribute \$1,000,000 to your company, meets with you.

John will only contribute this amount if he expects to get a return of 12% on his investment. Investors are interested in the number of years it will take for their investment to double.

## Using the Rule of 72

For John’s investment to double in value, it will take approximately six years.

## The Formula for the Rule of 72

For determining an expected doubling period or required rate of return, the rule of 72 can be applied in two different ways.

## Years To Double: 72 / Expected Rate of Return

By dividing 72 by the expected return, you can determine the time it will take for an investment to double. The formula is based on a single average rate over the life of the investment. Since all decimals represent an additional portion of a year, the findings are also the same for fractional results.

## Rate of Return: 72 / Years to Double

Divide 72 by the number of years required to double your investment to determine the expected rate of interest. A fraction or portion of a year can be handled by the formula; it does not have to be a whole number. Additionally, we assume that compound interest at that rate will be applied over the entire holding period to arrive at the expected rate of return.

## FAST FACT

The rule of 72 only applies in cases of compound interest, not simple interest. Simple interest is calculated using the daily interest rate and the number of days between payments. An interest rate is calculated on both the initial principal and the accumulated interest of previous periods.

## Rule of 72: How to Use It

It can be applied to anything that grows at a compound rate, such as population, macroeconomic numbers, charges, or loans. When the gross domestic product (GDP) grows at 4% per year, the economy will double in 72 / 4% = 18 years.

To demonstrate the long-term effects of fees that eat away at investment gains, the rule of 72 can be applied. In around 24 years, a mutual fund that charges 3% in annual expense fees will cut the investment principal in half. A borrower paying 12% interest on their credit card (or any other form of loan that charges compound interest) will double their debt in six years.

Inflation can also be calculated using this rule to determine how long it takes for money’s value to halve. If inflation is 6%, a given amount of money will be worth half in 12 years (72 / 6 = 12). Investing at 6% inflation will lose half its value in 18 years instead of 12 years if inflation decreases to 4%.

Moreover, the rule of 72 can be applied across all kinds of durations, provided the rate of return is compounded annually. A nation’s population will double in 72 months, or six years, if it increases by 1% per month. If the rate of interest per quarter is 4% (but it is compounded annually), doubling the principal will take (72 / 4) = 18 quarters or 4.5 years.

## Who Invented the Rule of 72?

As early as 1494, Luca Pacioli references the rule of 72 in his comprehensive mathematics book called Summa de Arithmetica. Despite not giving an explanation or derivation for the Rule, Pacioli depicts it as if it existed before his novel.

## How does the 72 Rule work?

• Here is how it works. Divide 72 by the investment’s projected annual return. Using this formula, we can approximate the number of years it will take for your money to double.
• For example, Considering an investment scheme that promises an annual compounded rate of return of 8%,
• The amount invested will double in approximately nine years (72 / 8 = 9). If your compound annual return is 8%, you will plug in 8 instead of 0.08, which would mean nine years rather than 900.
• The return on a \$1,000 investment takes nine years to double, then it becomes \$2,000 after nine years, \$4,000 after 18, \$8,000 after 27, etc.

## In what ways does the rule of 72 work?

• Rule of 72 formula provides an approximate but fairly accurate timeline since it simplifies a more complex logarithmic equation. To determine the exact doubling time, the entire calculation must be performed.
• In the case of an investment earning a compounded interest rate of r% per period, the formula to calculate the exact doubling time is:
• To find out how long it would take to double an investment that returns 8% annually, you would use the following equation:
• The length of time to the present is given by ln(2) / ln (1 + (8 / 100)) = 9.006 years
• You can see that this result is very close to the approximate value obtained by (72 / 8) = 9 years.

## The Rule of 72 versus the Rule of 73: What is the Difference?

• The rule of 72 is primarily applicable to interest rates or rates of return between 6% and 10%. Outside of this range, rates can be adjusted by adding or subtracting 1 from 72 for every 3 points the interest rate departs from the 8% threshold. As an example, 11% annual compounding interest is 3 percentage points higher than 8%.
• Adding 1 (for the 3 points above 8%) to 72 results in applying the rule of 73 for greater precision. For a 14% rate of return, it would be the rule of 74 (add 2 for 6 points higher), and for a 5% rate of return, it will mean reducing 1 (for 3 points lower) to result in the rule of 71.
• Let’s say you have an investment that offers a 22% return. Using the 72-year rule, the initial investment will double in 3.27 years. In the adjusted rule, the numerator should be 72 + 5 = 77 since (22 – 8) = 14, and (14 * 3) = 4.67 * 5. This gives 3.5 years, which indicates that you’ll have to wait an additional quarter to double your money compared to the basic rule of 72, which gives a result of 3.27 years. The logarithmic equation gives a period of 3.49, so the adjusted rule gives a more accurate result.
• 69.3 provides a more accurate result when daily or continuous compounding is used in the numerator. Many people adjust it to 69 or 70 to make calculations easier.

## Conclusion

Using the rule of 72, you can estimate how long it will take to double your money at a fixed annual interest rate. With an average rate of return and a current balance, you can determine how long it will take for your investments to double.

It is a valuable tool for both retirement planning and long-term financial planning. In addition to using a more in-depth projection method at some point, the rule of 72 serves as a great starting point.

## FAQs

### How does Rule 72 work, and what is its purpose?

The rule of 72 estimates how long it will take to double your money at a certain rate of return. Divide 72 by 4 to find how many years it will take for your money to double, for example, if your account earns 4 percent.

### In what way does the rule of 72 help?

The rule of 72 is a useful formula that is widely used for estimating the amount of time it will take for an investment to double at a given rate of return in 72 years. Alternatively, it can calculate the compounded annual rate of return on investment based on how long it will take to double the investment.

### In five years, how can I double my money?

If you want to work backward from your target date, you can reverse the rule of 72. Divide 72 by five to double your money in five years. It would take approximately 14.4 years for your money to double at 5% per year, based on the rule of 72.

### How does the 50-30-20 budget rule work?

As part of her book All Your Worth: The Ultimate Lifetime Money Plan, Senator Elizabeth Warren popularized the so-called “50/20/30 budget rule” (sometimes referred to as the “50-30-20 rule”). In general, after-tax income is allocated by spending it on needs, wants, and savings: 50% on needs, 30% on wants, and 20% on savings. 