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?

Question

Quizplus · Accepted Answer

Let "x" be the number of years it takes for China's real GDP per capita to be larger than that of the United States.
32,000(1.02)^x = 4,000(1.07)^x
(1.02)^x/(1.07)^x = 4/32
(1.02/1.07)^x = 0.125
x*log(1.02/1.07) = log(0.125)
x = log(0.125)/log(1.02/1.07)
x ≈ 43.8

So, it will take about 40 to 45 years for China's real GDP per capita to be larger than that of the United States. Answer: B.

Suppose That Real GDP Per Capita of the United States