Answer:
[tex]t=40.467 years[/tex]≅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=[tex]PV(1+r)^t[/tex]
where:
t is time
Future GDP=[tex]56,000(1+0.015)^t[/tex]
In case of China:
Present Value=$8,000
Increase=r=6.5%=0.065
Future GDP=[tex]PV(1+r)^t[/tex]
where:
t is time
Future GDP=[tex]8,000(1+0.065)^t[/tex]
We have to find time t when both countries have same future GDP:
[tex](Future GDP)_{US}=(Future GDP)_{China}[/tex]
[tex]56,000(1+0.015)^t[/tex]=[tex]8,000(1+0.065)^t[/tex]
Dividing equation by 8000:
[tex]7*(1+0.015)^t=(1+0.065)^t\\(\frac{1.065}{1.015})^t=7[/tex]
Taking Natural log (ln) on both sides:
[tex]ln 7=t*ln\frac{213}{203} \\t=40.467 years[/tex]
Time for Both countries have same Real GDP per capita is 40.467 years≅40.5 Years
