Real GDP per capita in the United States grew from about $6,000 in 1900 to about
ID: 1228107 • Letter: R
Question
Real GDP per capita in the United States grew from about $6,000 in 1900 to about $47, 041 in 2009, which represents an annual growth rate of 1.91 percent. Real-time data provided by Federal Reserve Economic Data (FRED), Federal Reserve Bank of Saint Louis. If the United States continues to grow at this rate, it will take years for real GDP per capita to double. (Enter your response rounded to two decimal places.) If government economic policies meant to stimulate economic growth result in the annual growth rate increasing to 2.66 percent, it will take years for real GDP per capita to double. (Enter your response rounded to two decimal places.)Explanation / Answer
If annual growth rate be R% and number of years be N, then
Final value = Initial value x (1 + R)N
(1 + R)N = Final value / Initial value
(1 + R)N = 2 (Since question refers to doubling of initial real GDP)
Taking natural logarith at each side,
N x ln (1 + R) = ln 2 = 0.6931
N = 0.6931 / ln (1 + R)
(a) R = 1.91%
N = 0.6931 / ln (1.0191) = 0.6931 / 0.0189 = 36.63 (years)
(b) R = 2.66%
N = 0.6931 / ln (1.0266) = 0.6931 / 0.0263 = 26.40 (years)
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