An economy starts off with a gdp per capita of $5,000. how large will the gdp per capita be if it grows at an annual rate of 2% for 20 years? 2% for 40 years? 4% for 40 years? 6% for 40 years?

To calculate the answer, remember that:

Starting Amount (1 + Growth Rate) Number of Years = Ending Amount

So under the various scenarios in the question we have:

$5,000 (1 +.02) 20 = $5,000 (1.49) = $7,450

$5,000 (1 +.02) 40 = $5,000 (2.20) = $11,000

$5,000 (1 +.04) 40 = $5,000 (4.80) = $24,000

$5,000 (1 +.06) 40 = $5,000 (10.29) = $51,450