Question

Real GDP per Capita in the US is currently $56,000 and grows at approximately 1.5% each year. Real GDP per Capita in China is currently $8,000 and grows at approximately 6.5% each year. If these growth rates continue, Real GDP per Capita for each country will be equal in how many years? (round to the nearest integer)

Answer 1

Future value (FV) of GDP after n years at growth rate of r is given by:

$FV = {PV}(1+r)^n$

According to question,

$FV_{USA} = FV_{China}$

$\Rightarrow 56000(1+0.015)^n = {8000}{(1+0.065)^n}$

$\Rightarrow \frac{(1+0.065)^n}{(1+0.015)^n} = 7$

$\Rightarrow (\frac{(1.065)}{(1.015)})^n = 7$$\Rightarrow (1.049)^n = 7$

$\Rightarrow nln (1.049) = ln 7 \Rightarrow n = ln 7/ ln 1.049 = 40.68$

i.e. After 41 years. Real GDP of both countries will be equal.