Use the following to answer questions :
Scenario: Growth Rates
Suppose that real GDP per capita of the United States is $32,000 and its growth rate is 2% per year. Real GDP per capita of China is $4,000, and its annual growth rate is 7%.
-(Scenario: Growth Rates) Look at the scenario Growth Rates. How many years will it take for China's real GDP per capita to be larger than real GDP per capita in the United States?

Question

Quizplus · Accepted Answer

We need to use the formula:
Y = A(1+g)^t
where Y is the real GDP per capita, A is the initial real GDP per capita, g is the annual growth rate, and t is the time in years.
We want to find out when China's real GDP per capita (Yc) will surpass the United States' real GDP per capita (Yu).
Yc = 4000(1+0.07)^t
Yu = 32000(1+0.02)^t
We need to solve for t when Yc is greater than Yu.
4000(1+0.07)^t > 32000(1+0.02)^t
Divide both sides by 4000(1+0.07)^t, then take the logarithm of both sides:
t > (ln(8) - ln(1.02))/(ln(1.07) - ln(1.02))
t > 42.5
Therefore, it will take about 42.5 years or approximately 40 to 45 years for China's real GDP per capita to be larger than real GDP per capita in the United States.

Use the Following to Answer Questions