Question

Assume real per capita GDP in North Metropolania is $6000 while in East Vice City it is $1500. The annual growth rate in North Metropolania is 2.33%, while in East Vice City it is 7%. How many years will it take for East Vice City to catch up to the real per capita GDP of North Metropolania?

Answer 1

It would take East Vice City 36 years to catch up to the real per capita GDP of North Metropolania

Step-by-step explanation:

Please find the detailed explanations and calculations as below:

Denote x is the number of years that needs to be found.

For East Vice City to catch up to the real per capita GDP of North Metropolania, we have the equation to show the real GDP of North Metropolania equals to that of East Vice City after x years as followed:

6,000 x 1.0233^x = 1,500 x 1.07^x <=> 4 x 1.0233^x = 1.07^x <=> x = 36 years