Question

The real per capita GDP in country X is 4 times of that in country Y. The annual growth rate in country X is 2.33%, while in country Y it is 7%. How many years will it take for country Y to catch up to the real per capita GDP of country X?

Answer 1

Answer:

It will take a little over 30 years for country Y's real GDP per capita to catch up with country X's real GDP per capita

Explanation:

we can assume that country X has a real GDP per capita of 100, while country Y's real GDP per capita is 25. Country X's annual growth rate is 2.33% and country Y's is 7%.

The easiest way to determine now long it will take country Y's real GDP per capita to double, or quadruple, is the rule of 72. But since country X's growth rate is 2.33%, we must adjust this rule by -2, and use the rule of 70. The rule of 72 is very exact for 8% calculations, but it must be adjusted by +/- 1 for every 3% points away from 8%.

• it will take 70/2.33 = 30 years for country X's real GDP per capita to double = 200
• it will take 72/7 = 10.29 years for country Y's real GDP per capita to double = 50, another 10.29 years to equal 100, and 10.29 more years to equal 200. Roughly in about 30.86 years will country Y's GDP per capita = 200, which is similar to country X's real GDP per capita at that time.

Answer 2

Answer:

It will take 30 years for country Y’s GDP to catch up with that of country X

Explanation:

In this question. We are asked to calculate the number of years it will take a certain country Y to catch up with the GDP of a certain country X, given the annual growth rate in both countries.

We calculate the number of years as follows;

Firstly, we assign a variable to the value of the real GDP of country Y

let real

Let the real GDP of the country Y be n. This means that the GDP of country C will be 4 * n = 4n

With a 7% growth rate annual, country Y's Real GDP will be doubled in 70/7 = 10 years and;

With annual growth rate of 2.33% ,country x's Real GDP doubles in 70/2.33 = 30 years.(Approx)

Now in next 30 years x's Real GDP will be = 2x4n = 8n

and Y's Real GDP in next 30 years will be = 2x2x2xn = 8n.

thus , it will take 30 years to country Y to catch up to the level of country x.