Question

In the CIA World Fact Book, GDP per capita in the United States in 2010 was approximately $47,400. The formula for growth used in that spreadsheet for any given year, yt, is yt = y0 (1 + g)t, where y0 is the value of GDP in the beginning year, yt is the value of GDP for the specific year in question, and t is the number of years after y0. If y0 is GDP per capita in 2010 and the economy continues to grow at approximately 3% as it did in 2010, what will be the value of GDP per capita in ten years?

Answer 1

Value of GDP per capita in 10 years i.e value of GDP per capita in 2020 is given by,

$y_{10} = y0 (1+gy)^{10}$ ( t=10 since y0 is the GDP per capita in 2010)

$y_{10} = \$47,400(1+0.03)^{10}\\ y_{10} = \$ 47,400\times 1.3439\\ = \$ 63,700.86$

Therefore, GDP per capita in 2020$= \$ 63,701$