Question

What annual growth rate is needed for a country to double its output in 7 years? In 35 years? In 70 years? In 140 years?

Short answer

• The country will require 10 percent of growth to double its economy in 7 years.
• The country will require 2 percent of growth to double its economy in 35 years.
• The country will require 1 percent of growth to double its economy in 70 years.
• The country will require 0.5 percent of growth to double its economy in 140 years.

Step-by-step solution

Step 1. Defining the concept “rule of 70”.

Economists use the concept “rule of 70” to evaluate the approximate number of years an economy will take to double its size. The mathematical expression under the rule of 70 is given below:

$ApproximatenumberofyearsrequiredtodoubletherealGDP=\frac{70}{Annualpercentagerateofgrowth}$

Step 2. Calculating annual growth rates

The required annual growth rate for a country to double its output can be calculated by using the “rule of 70” formula.

• The required annual percentage growth for a country to double its output in 7 years is:

$$\begin{gathered} Annualpercentagerateofgrowth=\frac{70}{7} \\ =10percent \end{gathered}$$

The required annual growth rate is 10 percent.

• The required annual percentage growth for a country to double its output in 7 years is:

$$\begin{gathered} Annualpercentagerateofgrowth=\frac{70}{35} \\ =2percent \end{gathered}$$

The required annual growth rate is 2 percent.

• The required annual percentage growth for a country to double its output in 7 years is:

$$\begin{gathered} Annualpercentagerateofgrowth=\frac{70}{70} \\ =1percent \end{gathered}$$

The required annual growth rate is 1 percent

• The required annual percentage growth for a country to double its output in 7 years is:

$$\begin{gathered} Annualperce\tan gerateofgrowth=\frac{70}{140} \\ =0.5percent \end{gathered}$$

The required annual growth rate is 0.5 percent.