Rule of 72 Calculator

How to Use the Rule of 72 Calculator

The Rule of 72 is a simple and quick way to estimate how long it will take for an investment to double or what interest rate is needed to double your money in a specific time period. This calculator provides two main functions:

1. Find Time to Double

This function calculates how long it will take for your investment to double, given a specific interest rate.

Formula: $$T = \frac{72}{r}$$

Where:

• T = Time to double the investment (in years)
• r = Annual interest rate (as a percentage)

2. Find Required Rate

This function calculates the interest rate needed to double your investment in a specific number of years.

Formula: $$r = \frac{72}{T}$$

Where:

• r = Required annual interest rate (as a percentage)
• T = Time to double the investment (in years)

Calculation Steps

For Finding Time to Double:

1. Enter the initial investment amount.
2. Enter the annual interest rate.
3. Apply the formula: T = 72 / r
4. The result is the approximate number of years it will take for the investment to double.

For Finding Required Rate:

1. Enter the initial investment amount.
2. Enter the desired number of years to double the investment.
3. Apply the formula: r = 72 / T
4. The result is the approximate annual interest rate needed to double the investment in the specified time.

Example Calculation

Let's calculate the time needed to double an investment of $10,000 at an annual interest rate of 6%.

Step 1: Identify the values

• Initial Investment = $10,000
• Annual Interest Rate (r) = 6%

Step 2: Apply the formula

$$T = \frac{72}{r} = \frac{72}{6} = 12 \text{ years}$$

Step 3: Interpret the result

It will take approximately 12 years for the $10,000 investment to double to $20,000 at a 6% annual interest rate.

Visual Representation

This diagram illustrates how a $10,000 investment grows over 12 years at a 6% annual interest rate, doubling to approximately $20,000 by the end of the period. The Rule of 72 provides a quick estimate for this doubling time, which closely matches the actual exponential growth of the investment.