Question

A mathematical approximation called the rule of 70 tells us how long it

will take for something to double in size if it grows at a constant rate. The

doubling time is approximately equal to the number 70 divided by the percentage

rate of growth. Thus, if Panama’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 Panama in 2017 was about \(15,000

per person, while it was about \)60,000 per person in the United States. If real GDP

per person in Panama grows at the rate of 5 percent per year, about how long will ittake Panama’s real GDP per person to reach the level that the United States was

at in 2017? (Hint: How many times would Panama’s 2017 real GDP per person

have to double to reach the United States’ 2017 real GDP per person?)

Short answer

Panama’s real GDP per person will take 28 years to reach the United States’ level in

2017.

Step-by-step solution

Number of times Panama’s GDP per person should double to reach thelevel of US’s GDP

The GDP per person in the US is $60,000 and that in Panama is $15,000.

$$\begin{gathered} \frac{GD{P}_{US}}{GD{P}_{Panama}}=\frac{60,000}{15,000} \\ GD{P}_{US}=4\times GD{P}_{Panama} \end{gathered}$$

The GDP per person in the US is four times that in Panama.

The GDP per person in Panama will double to $30,000 in the first phase, and the GDP per person will reach $60,000 in the second phase.

Therefore, the GDP per person in Panama will have to double twice to reach the United States’ 2017 real GDP per person.

Time taken to double Panama’s GDP per person (to reach $60,000)

According to the rule of 70, the doubling rate of GDP per person in Panama will be as follows:

$DoublingRate=\frac{70}{5}=14$

Thus, the GDP per person in Panama doubles every 14 years.

So to reach $60,000, the GDP per person in Panama will take (14 × 2)= 28 years.