Rules of 70 and 72: Tools for Growth and Decline

The Rule of 70 and Rule of 72 are shortcuts to estimate how long it takes for something to double, or shrink, based on its growth or decline rate. These rules work whether the changes happen continuously or at specific intervals.

The Rule of 70

The Rule of 70 is ideal for continuous change, where growth or decline happens steadily over time. Think of situations like:

• A business experiencing a consistent drop in daily sales.
• An investment that compounds interest (or losses) monthly or daily.

To estimate how long it takes for a value to double (or halve), divide 70 by the percentage rate, ignoring the percentage sign.

Example 1: Continuous Growth
A startup’s monthly user base is growing steadily at 7% annually due to effective marketing. Using the Rule of 70:
70 ÷ 7 = 10 years
The user base will double in about 10 years at this rate.

Example 2: Continuous Shrinking
A retail store’s foot traffic is declining by 5% annually due to competition from e-commerce. Using the Rule of 70:
70 ÷ 5 = 14 years
At this rate, the store’s foot traffic will be cut in half in roughly 14 years.

The Rule of 72

The Rule of 72 is best for changes happening at regular intervals, like once a year. It’s commonly applied in situations such as:

• Annual raises or bonuses.
• Periodic reductions in costs or budgets.

To calculate doubling or halving time, divide 72 by the annual growth or decline rate.

Example 1: Annual Growth
An employee gets a 6% annual raise. Using the Rule of 72:
72 ÷ 6 = 12 years
It will take about 12 years for their salary to double.

Example 2: Annual Shrinking
A city’s population is decreasing by 3% annually due to migration. Using the Rule of 72:
72 ÷ 3 = 24 years
At this rate, the population will halve in approximately 24 years.

How to Choose the Right Rule

The type of change determines which rule to use:

• Use the Rule of 70 for continuous growth or decline spread across time.
• Use the Rule of 72 for annual or periodic growth or decline.

Expanded Examples

Example 1: Continuous Shrinking with Rule of 70
A newspaper’s subscription base is declining by 4% annually due to the shift to digital media. Since the decline is continuous, apply the Rule of 70:
70 ÷ 4 = 17.5 years
It will take about 17.5 years for the subscription base to shrink to half its current size.

Example 2: Annual Growth with Rule of 72
A savings account earns 8% annual interest. Using the Rule of 72:
72 ÷ 8 = 9 years
The account’s balance will double in 9 years if no withdrawals are made.

Example 3: Comparing Both Rules for Growth and Shrinking
A company’s revenue grows continuously at 5%, but its operating expenses shrink at 3% annually due to cost-cutting.

• Revenue Growth: Use the Rule of 70.
  70 ÷ 5 = 14 years
  Revenue will double in 14 years.
• Expense Reduction: Use the Rule of 72.
  72 ÷ 3 = 24 years
  Operating expenses will halve in 24 years.

Why These Rules Matter

The Rules of 70 and 72 are simple yet powerful tools for estimating doubling or halving time. They’re not limited to business or finance, they can also be applied to population studies, environmental changes, or even personal budgets. Whether you’re planning for growth or responding to decline, these rules provide a quick way to understand the long-term impact of changes and guide your decision-making.

Until the next one,

J