Economy Growth Comparison: 4% vs 1% Annual Rate

To calculate the ratio between the two economies' real GDP after a certain number of years, we need to use the formula for compound interest.

For Economy A, after 10 years, the growth rate is 4%, so the real GDP is multiplied by (1 + 0.04)^10.

For Economy B, after 10 years, the growth rate is 1%, so the real GDP is multiplied by (1 + 0.01)^10.

The ratio between the two economies after 10 years is (1 + 0.04)^10 / (1 + 0.01)^10.

Using a calculator, we find that the ratio after 10 years is approximately 1.488.

Similarly, we can calculate the ratio after 20 years and 30 years:

After 20 years: (1 + 0.04)^20 / (1 + 0.01)^20 ≈ 1.797

After 30 years: (1 + 0.04)^30 / (1 + 0.01)^30 ≈ 2.165

Therefore, the ratio between the two economies' real GDP after 10 years is approximately 1.488, after 20 years is approximately 1.797, and after 30 years is approximately 2.165.