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,

$GDP_{US}\times[1+growth_{US}]^n<GDP_{China}\times[1+growth_{China}]^n$

On plugging-in the values,

$\Rightarrow32000\times(1+0.02)^n<4000\times(1+0.07)^n$

On solving the values we get,

$\Rightarrow8<\frac{(1+0.07)^n}{(1+0.02)^n}$

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