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

Answer 1

Answer:

$t=40.467 years$≅40.5 years

Time for Both countries have same Real GDP per capita is 40.467 years≅40.5 Years

Explanation:

In case of US:

Present Value=$56,000

Increase=r=1.5%=0.015

Future GDP=$PV(1+r)^t$

where:

t is time

Future GDP=$56,000(1+0.015)^t$

In case of China:

Present Value=$8,000

Increase=r=6.5%=0.065

Future GDP=$PV(1+r)^t$

where:

t is time

Future GDP=$8,000(1+0.065)^t$

We have to find time t when both countries have same future GDP:

$(Future GDP)_{US}=(Future GDP)_{China}$

$56,000(1+0.015)^t$=$8,000(1+0.065)^t$

Dividing equation by 8000:

$7*(1+0.015)^t=(1+0.065)^t\\(\frac{1.065}{1.015})^t=7$

Taking Natural log (ln) on both sides:

$ln 7=t*ln\frac{213}{203} \\t=40.467 years$

Time for Both countries have same Real GDP per capita is 40.467 years≅40.5 Years