Question

Assume real per capita GDP in North Metropolania is $10000 while in East Quippanova it is $2500. The annual growth rate in North Metropolania is 2.33%, while in East Quippanova it is 7%. How many years will it take for East Quippanova to catch up to the real per capita GDP of North Metropolania? Choose one: A. about 10 years B. about 30 years C. about 40 years D. about 120 years E. East Quippanova will never be able to catch up with North Metropolania.

Answer 1

Option (B) is correct.

Step-by-step explanation:

Real per capita GDP in North Metropolania(A) = $10,000

Real per capita GDP in East Quippanova(B) = $2,500

Annual growth rate in North Metropolania(C) = 2.33%

Annual growth rate in East Quippanova(D) = 7%

`A*(1+C)^(n) = B*(1+D)^(n)`

`10,000*(1+0.0233)^(n) = 2,500 *(1+0.07)^(n)`

`((1.07)/(1.0233))^(n)=(10,000)/(2,500)`

`(1.0456)^(n)=4`

Taking the Natural Log of both sides,

n ln(1.0456) = ln(4)

n × 0.0446 = 1.3863

n = 31.08

Thus, it will take 31.08 years for East Quippanova to catch up to the real per capita GDP of North Metropolania.