Question

Richland’s real GDP per person is $5,000, and Poorland’s real GDP per person is $2,500. However, Richland’s real GDP per person is growing at 2 percent per year, and Poorland’s is growing at 4 percent per year. Compare real GDP per person in the two countries after 10 years and after 20 years. Approximately how many years will it take Poorland to catch up to Richland? Instructions: Enter your responses as whole numbers. GDP per person GDP per person after 10 years GDP per person after 20 years Richland $ $ Poorland $ $ Poorland will catch up to Richland in years.

Answer 1

Real GDP per person in Richland is $5,000, and $2,500 in Poorland. Richland’s real GDP per person is growing at 2 percent per year that of Poorland’s is growing at 4 percent per year.

After 10 years we have

Real GDP per person in Richland = 5000 x (1 + 2%)^10 = $6,095

Real GDP per person in Poorland = 2500 x (1 + 4%)^10 = $3,701

After 20 years we have

Real GDP per person in Richland = 5000 x (1 + 2%)^20 = $7,430

Real GDP per person in Poorland = 2500 x (1 + 4%)^20 = $5,478

Cpmpare the two rates and find the matching year

5000 x (1 + 2%)^n = 2500 x (1 + 4%)^n

5000/2500 = 1.04^n/1.02^n

ln(2) = n x ln(1.04/1.02)

n = ln(2)/ln(1.04/1.02) = 36

It takes 36 years for Poorland to catch up to Richland.