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

Answer:

Option (B) is correct.

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%

$A\times(1+C)^{n} = B\times(1+D)^{n}$

$10,000\times(1+0.0233)^{n} = 2,500 \times(1+0.07)^{n}$

$(\frac{1.07}{1.0233})^{n}=\frac{10,000}{2,500}$

$(1.0456)^{n}=4$

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.