5 Between 1975 and 2010 Chinas GDP Per Capita averaged 8 For

5. Between 1975 and 2010, China\'s GDP Per Capita averaged 8%. For the same time-period, the US rate was 1 .8%. In 2010, China\'s PC GDP was $7800, and in the US it was $42,500. Assuming both countries continue to grow at the same rates, in what year will China overtake the US in terms of Per-Capita GDP

Solution

Let N be the number of years after year 2010 when GDP per capita becomes equal in China and US. Therefore,

$7,800 x (1.08)^N = $42,500 x (1.018)^N

(1.08 / 1.018)^N = $42,500 / $7,800 = 5.4487

(1.0609)^N = 5.4487

Taking natural logarithm on each side,

N x ln 1.0609 = ln 5.4487

N x 0.0591 = 1.6954

N = 28.69

Therefore, per capita GDP will be equal after 28.69 years, meaning that China\'s per capita GDP will overtake US per capita GDP after 29 years.

Required year = 2010 + 29 = year 2039