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 long will it take China's real GDP per capita to catch up with that of United States?

Answer 1

40 years

Step-by-step 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
`\frac{\textup{70}}{\textup{Growth rate}}` years

Therefore,

The United States GDP will double in =
`\frac{\textup{70}}{\textup{2}}` = 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 =
`\frac{\textup{70}}{\textup{7}}` = 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