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 long will it take china's real gdp per capita to catch up with that of united states?

40 years

Explanation:

Given:

Per capita GDP of United states = $32,000

Per capita GDP of China = $4,000

Growth rate of United states = 2%

Growth rate of China = 7%

Now, By the rule of 70 , the GDP will double in years

Therefore,

The United States GDP will double in =  = 35 years

Thus,

The GDP of united states in 35 years will be (2 × $32,000 ) = $64,000

this is equals to the 16 times the current GDP of the China

Now,

The China GDP will double in = = 10 years

Therefore,

The GDP of china will be

2 × $4,000 in 10 years   = $8,000

in 20 years  = 2 × $8,000 = $16,000  ( i.e 4 times)

in 30 years  = 2 × $16,000 = $32,000  ( i.e 8 times)

in 40 years  = 2 × $32,000 = $64,000  ( i.e 16 times)

Hence, it will take 40 years for China to catch up with the united states