Question

In 2016 GDP of the United States was $18 trillion, whereas that of China was $9 trillion. If China's growth rate of 7 percent per year is sustained and the US grows at 2 percent per year, when will China surpass the US in terms of GDP? (show calculations) 3

Answer 1

Let N be the number of years after which GDP will be equal in both countries. Then

$18 trillion x (1.02)^N = $9 trillion x (1.07)^N

[(1.07)^N] / [(1.02)^N] = $18 trillion / $ trillion

[(1.07 / 1.02)^N] = 2

(1.0490)^N = 2

Taking natural logarithm on both sides,

N x ln 1.0490 = ln 2

N x 0.0478 = 0.6931

N = 14.5 years

Therefore, China will surpass US after 14.5 years, i.e. in year 15.