If the annual real GDP per capita in the United States is currently $50,000 and growing at 2.5 percent per year, how many years will it take to reach an annual real GDP per capita of $100,000?

Question

Quizplus · Accepted Answer

Using the formula for compound interest, we can find the time it will take for the GDP per capita to double:

$50,000 * (1 + 0.025)^t = $100,000

Simplifying, we get:

(1 + 0.025)^t = 2

Taking the natural log of both sides:

t * ln(1.025) = ln(2)

t = ln(2) / ln(1.025)

t ≈ 27.7 years

Therefore, it will take approximately 28 years for the annual real GDP per capita in the United States to reach $100,000.

If the Annual Real GDP Per Capita in the United