Assume real per capita GDP in North Metropolania is $8,000 while in East Vice City it is $2,000. 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

31 years

Explanation:

we have to prepare two future value equations:

next we must equal them:

$8,000 x (1 + 0.0233)ⁿ = $2,000 x (1 + 0.07)ⁿ

4 x (1 + 0.0233)ⁿ = (1 + 0.07)ⁿ

4 = 1.07ⁿ / 1.0233ⁿ = (1.07 / 1.0233)ⁿ

4 = 1.0456367ⁿ

log4 = n x log1.0456367

0.602 = n x 0.01938

n = 0.602 / 0.01938 = 31.06 ≈ 31 years

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