Chapter 29: Problem 966

What is the rule of $72 ?$

Short Answer

Expert verified

The Rule of 72 is a formula used to estimate the number of years required to double the value of an investment or money in an account, based on a fixed annual rate of return. The formula is: \[ Years \,to\, Double = \frac{72}{Interest \, Rate} \] For example, if the annual interest rate is 6%, it would take approximately 12 years for the investment to double in value. This is an approximation and may not be as accurate for extremely high or low interest rates.

Step by step solution

Introducing the Rule of 72

The Rule of 72 is a quick and easy method to estimate the number of years it takes for an investment or an amount of money to double at a fixed annual interest rate. It's an approximation, but it's quite useful for getting a rough idea of the time required for an investment to grow.

The Formula

The formula for the Rule of 72 is simple: \[ Years \,to\, Double = \frac{72}{Interest \, Rate} \] Where "Years to Double" is the estimated time for the investment to double and "Interest Rate" is the annual interest rate (expressed as a percentage).

Example

Let's go through an example to show how the Rule of 72 works. Suppose you invest $1,000 in an account with an annual interest rate of 6% (0.06 as a decimal). We can use the Rule of 72 to estimate how long it will take for the investment to double in value. Apply the Rule of 72 formula: \[ Years \,to\, Double = \frac{72}{Interest \, Rate} \] \[ Years \,to\, Double = \frac{72}{6} \]

Calculate the Result

Now we can perform the division: \[ Years \,to\, Double = 12 \] So, using the Rule of 72, it would take approximately 12 years for the $1,000 investment to double in value at an annual interest rate of 6%. Keep in mind that the Rule of 72 is an approximation and may not be as accurate for extremely high or low interest rates. It is, nevertheless, a useful tool for getting quick insights into the growth potential of various investments.

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What is the rule of \(72 ?\)

Short Answer

Step by step solution

Introducing the Rule of 72

The Formula

Example

Calculate the Result

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