Question

Suppose that real GDP per capita of the United States is $32,000 and its growth rate is 2% per year and that real GDP per capita of China is $4,000, and its annual growth rate is 7%. How many years will it take for China's real GDP per capita to be larger than real GDP per capita in the United States

Answer 1

Given:

Real GDP of US = 32000

Growth rate of US = 2%

Real GDP of China = 4000

Growth rate of China = 7%

To find:

Number of years taken for China's real GDP per capita to be larger than real GDP per capita in the United States.

Solution:

The formula to calculate the years is,

`GDP_(US)*[1+growth_(US)]^n<GDP_(China)*[1+growth_(China)]^n`

On plugging-in the values,

`\Rightarrow32000*(1+0.02)^n<4000*(1+0.07)^n`

On solving the values we get,

`\Rightarrow8<((1+0.07)^n)/((1+0.02)^n)`

Therefore, we can clearly identify that number of years is greater than 40 and less than 45.