The Rule of 72 : Definition, Formula, and How to Use it

What is the Rule of 72?

The rule of 72 is the formula which is used to calculate in how much time our investment is going to be doubled in the given annual rate of return. Simply it can be calculate by dividing the 72 from annual rate of return and you will get the time period (years) in which your amount is going to be doubled.

If you want to know in how much your investment or capital you are having will be doubled so you can apply rule of 72.
Also if you want to find out the annual rate of return in which you money can be for the given number of year we can also apply the rule of 72 their.

The Formula of Rule of 72

The Rule of 72 can be used in two main ways:

1. To Calculate Time (When Rate is Known)

Use this to estimate how long it will take for an investment to double.
Formula:

$text{Time to double} = frac{72}{text{Annual Interest Rate (%)}}$
Example:
At 6% annual return:
Time = 72 ÷ 6 = 12 years

2. To Calculate Rate (When Time is Known)

Use this to estimate the annual interest rate required to double an investment in a given time.
Formula:

$text{Rate} = frac{72}{text{Time (Years)}}$
Example:
To double in 8 years:
Rate = 72 ÷ 8 = 9% per year

These two applications make the Rule of 72 a flexible and powerful tool for financial planning.

Example of The Rule of 72

Example 1:

If an investment grows at an annual interest rate of 6%, how long will it take to double?

text{Time to double} = frac{72}{6} = 12 , text{years}

So, at a 6% annual return, your investment will double in approximately 12 years.

Example 2:

If an investment grows at 8% per year, how long will it take to double?

text{Time to double} = frac{72}{8} = 9 , text{years}

At 8%, your investment will double in around 9 years.

Example 3:

If your money is earning 4% annual interest, how long will it take to double?

text{Time to double} = frac{72}{4} = 18 , text{years}

At 4%, your investment will double in approximately 18 years.

Key Points:

The Rule of 72 is a quick and easy method to estimate growth.
It assumes a constant rate of return and doesn’t factor in inflation or taxes.
Useful for evaluating the potential of investments at a glance.

Practical Uses of the Rule of 72 in Finance

The Rule of 72 is a handy tool for making quick estimates in various financial scenarios involving growth or decay. Here are some practical applications:

1. Investment Growth

To estimate how long it will take for an investment to double at a fixed annual return.
Example: If an investment earns a 6% return annually, it will double in 72 ÷ 6 = 12 years.

2. Required Rate of Return

To determine the annual return rate needed to double your investment in a specific time frame.
Example: To double your money in 8 years, you need a rate of 72 ÷ 8 = 9% per year.

3. Inflation Impact

To calculate how long it takes for the purchasing power of money to halve due to inflation.
Example: At a 3% inflation rate, the purchasing power of money will halve in 72 ÷ 3 = 24 years.

4. Debt Doubling

To estimate how quickly debt will double if left unpaid at a fixed interest rate.
Example: At a 10% interest rate, unpaid debt will double in 72 ÷ 10 = 7.2 years.

5. Economic Growth Projections

To estimate how long it will take for an economy (e.g., GDP) to double at a steady growth rate.
Example: If GDP grows at 4% annually, it will double in 72 ÷ 4 = 18 years.

6. Financial Planning

Helps investors and planners quickly evaluate the potential growth of savings, investments, or retirement funds.
Example: A retirement fund earning 8% per year will double in 72 ÷ 8 = 9 years.

7. Energy Consumption or Resource Usage

Used in industries like energy or commodities to estimate how quickly usage doubles based on demand growth.
Example: If energy consumption grows by 5% annually, it will double in 72 ÷ 5 = 14.4 years.

Why It’s Useful:

Quick Estimation: Provides a simple way to make rough calculations without complex tools.
Versatility: Applicable to various growth scenarios like investments, inflation, or debts.
Decision-Making: Assists in comparing financial options and setting realistic goals.

Who invented the Rule of 72?

While the exact inventor of the Rule of 72 is uncertain, its roots are tied to the development of compound interest theory and practical approximations in finance, possibly dating back to Luca Pacioli or even earlier mathematical works. It remains one of the most widely used tools for financial calculations today.

Rule of 72 Table (For 1% to 10% Rates)

Annual Rate (%)	Time to Double (Years)
1%	72 ÷ 1 = 72 years
2%	72 ÷ 2 = 36 years
3%	72 ÷ 3 = 24 years
4%	72 ÷ 4 = 18 years
5%	72 ÷ 5 = 14.4 years
6%	72 ÷ 6 = 12 years
7%	72 ÷ 7 = 10.3 years
8%	72 ÷ 8 = 9 years
9%	72 ÷ 9 = 8 years
10%	72 ÷ 10 = 7.2 years

Similar Rules like The Rule of 72

Some other rules and formulas that are similar to the Rule of 72 and are used to simplify financial calculations. Some of these rules are focused on different aspects of growth, interest, and time. Here are a few examples:

The Rule of 69 (or 69.3)

The Rule of 69 is similar to the Rule of 72 but is used when the compounding frequency is continuous (i.e., compounding happens continuously rather than annually).
Formula:
$text{Time to Double} = frac{69.3}{text{Interest Rate (%)}}$
This rule is typically used in more advanced financial contexts where interest compounds continuously.

The Rule of 114

The Rule of 114 helps estimate how long it will take for an investment to triple at a given annual interest rate.
Formula:
$text{Time to Triple} = frac{114}{text{Interest Rate (%)}}$
Example: If an investment grows at 6% per year, it will triple in 114 ÷ 6 = 19 years.

The Rule of 144

The Rule of 144 is used to estimate how long it will take for an investment to quadruple (4x) based on a given rate of return.
Formula:
$text{Time to Quadruple} = frac{144}{text{Interest Rate (%)}}$
Example: At an interest rate of 8%, the time to quadruple is 144 ÷ 8 = 18 years.

The Rule of 70

The Rule of 70 is used to estimate the time it will take for an investment to halve in value, typically in the case of inflation or declining returns.
Formula:
$text{Time to Halve} = frac{70}{text{Inflation Rate (%)}}$
Example: If inflation is 4%, the time to lose half of the value of money is 70 ÷ 4 = 17.5 years.

Doubling Time Formula (Exact)

The exact formula for doubling time (without approximation) using logarithms is:
$T = frac{ln(2)}{ln(1 + frac{r}{100})}$
Where
$T$
is the time to double, and
$r$
is the interest rate. This formula gives a more accurate result than the Rule of 72.

Summary of Similar Rules:

Rule	Purpose	Formula
Rule of 72	Time to double	$frac{72}{text{Rate (%)}}$
Rule of 69	Time to double (continuous compounding)	$frac{69.3}{text{Rate (%)}}$
Rule of 114	Time to triple	$frac{114}{text{Rate (%)}}$
Rule of 144	Time to quadruple	$frac{144}{text{Rate (%)}}$
Rule of 70	Time to halve (inflation/decline)	$frac{70}{text{Inflation Rate (%)}}$

These rules are all designed to provide quick estimates of growth, decay, or other financial changes over time. They’re especially useful for quick mental calculations or rough estimates.