Question

A mathematical approximation called the rule of 70 tells us that the number of years that it will take something that is growing to double in size is approximately equal to the number 70 divided by its percentage rate of growth. Thus, if Mexico’s real GDP per person is growing at 7 percent per year, it will take about 10 years (= 70/7) to double. Apply the rule of 70 to solve the following problem. Real GDP per person in Mexico in 2005 was about $11,000 per person, while it was about $44,000 per person in the United States. If real GDP per person in Mexico grows at the rate of 5 percent per year, about how long will it take Mexico’s real GDP per person to reach the level that the United States was at in 2005? (Hint: How many times would Mexico’s 2005 real GDP per person have to double to reach the United States’ 2005 real GDP per person?)

Answer 1

Answer:

The answer is: It will take Mexico 28 years

Explanation:

In 2005, Mexico´s GDP per capita (MGDPpC) was only $11,000 which represented one fourth of the United States´ GDP per capita (USGDPpC) of $44,000.

The ratio of GDP per Capita between Mexico and the United States is 1:4

So when MGDPpC doubles the first time, the ratio will be 2:4 (or 1:2), so when it doubles again the ratio will b 1:1. So in order for MGDPpC to equal the amount of USGDPpC in 2005, it would need to double twice.

To find out how many years it will take Mexico to double its GDP per capita once, we must divide 70 by 5, which equals 14 years.

Since it takes Mexico 14 years to double its GDP per capita, it will take them 28 years to double it twice.