Suppose that real GDP per capita of Canada is $32 000 and its growth rate is 2% per year and that real GDP per capita of China is $4 000,and its annual growth rate is 7%.How many years will it take for China's real GDP per capita to be larger than real GDP per capita in Canada?

Question

Quizplus · Accepted Answer

Using the formula for calculating the future value of an asset with continuous compounding:

FV = PV e^(r * t)

where: 
FV = future value 
PV = present value 
r = annual growth rate 
t = time period

We can set up the inequality:

$4,000 e^(0.07t) > $32,000 e^(0.02t)

Simplifying:

e^(0.05t) > 8

Taking the natural log of both sides:

0.05t > ln(8)

t > ln(8)/0.05 ≈ 35.5

Therefore, it will take about 40-45 years for China's real GDP per capita to be larger than real GDP per capita in Canada.

Suppose That Real GDP Per Capita of Canada Is $32