Final answer:
To calculate the future incomes, apply the compound growth formula. After 20 years, South Korea's income is approximately $21,911, growing by a factor of about 2.19, while the United States' income is roughly $12,202, growing by about 1.22 times the starting amount.
Step-by-step explanation:
To calculate the future income of South Korea and the United States with different annual growth rates over a 20-year period, we'll use the formula for compound growth, which is:
Future Value = Present Value × (1 + Growth Rate)^Years
For South Korea, the calculation is as follows:
× (1 + 0.04)^20
Future Value of South Korea = $10,000 × (1.04)^20 = $10,000 × 2.1911 $≈ $21,911
For the United States, the calculation is as follows:
Future Value of United States = $10,000 × (1.01)^20 = $10,000 × 1.2202 $≈ $ 12,202
South Korea's income will have grown by a multiple of approximately 2.19 (or 219%) over 20 years, whereas the United States' income will have grown by a multiple of approximately 1.22 (or 122%) in the same period.
Projecting incomes based on growth rates and understanding the compound effect over time can significantly influence a country's economic forecasting.