Per Capita Federal Debt In 2014, the federal debt was about...

Per Capita Federal Debt In 2014, the federal debt was about $17.5 trillion. In 2014, the U.S. population was about 317 million. Assuming that the federal debt is increasing about 6.4% per year and the U.S. population is increasing about 0.7% per year, determine the per capita debt (total debt divided by population) in 2030.

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Key Concepts

Exponential Growth

Exponential growth describes the process by which a quantity increases by a constant percentage over equal time intervals, resulting in growth that accelerates over time. This concept is essential for understanding how both the federal debt and the population evolve over multiple years, as each year builds upon the previous year's value.

Compound Growth Formula

The compound growth formula, represented as A = P × (1 + r)^n, is used to calculate the future value of a quantity that grows at a fixed rate per period. In this context, it allows calculation of the estimated federal debt and population in 2030 by applying the respective annual growth rates over a given number of years.

Per Capita Analysis

Per capita analysis involves dividing a total value by the number of individuals in a population, providing a measure of how much of that quantity corresponds to each individual. This method is crucial for understanding the individual burden of the federal debt by relating the total debt to the estimated future population.

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