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Consider two countries, A and B. Country A has a real GDP per capita of $20 000. Country B has a real GDP per capita of $5000. If Country A grows at an average annual rate of 2% and Country B grows at an average annual rate of 8%, which of the following statements is correct?Group of answer choicesCountry B‘s real GDP will be greater than Country A’s real GDP after 20 yearsCountry B‘s real GDP will be greater than Country A’s real GDP after 10 yearsCountry B‘s real GDP will be less than Country A’s real GDP after 40 yearsCountry B‘s real GDP will be greater than Country A’s real GDP after 30 years

Question

Consider two countries, A and B. Country A has a real GDP per capita of 20000.CountryBhasarealGDPpercapitaof20 000. Country B has a real GDP per capita of 5000. If Country A grows at an average annual rate of 2% and Country B grows at an average annual rate of 8%, which of the following statements is correct?Group of answer choicesCountry B‘s real GDP will be greater than Country A’s real GDP after 20 yearsCountry B‘s real GDP will be greater than Country A’s real GDP after 10 yearsCountry B‘s real GDP will be less than Country A’s real GDP after 40 yearsCountry B‘s real GDP will be greater than Country A’s real GDP after 30 years

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Solution

To answer this question, we need to calculate the future real GDP per capita for both countries using the formula for compound interest, which is:

Future Value = Present Value * (1 + growth rate) ^ number of years

For Country A: Future Value = $20,000 * (1 + 0.02) ^ number of years

For Country B: Future Value = $5,000 * (1 + 0.08) ^ number of years

We need to find out when the future value of Country B's real GDP per capita will exceed that of Country A's.

Let's calculate:

After 10 years: Country A = 20,000∗(1+0.02)10=20,000 * (1 + 0.02) ^ 10 = 24,394.64 Country B = 5,000∗(1+0.08)10=5,000 * (1 + 0.08) ^ 10 = 10,794.62

After 20 years: Country A = 20,000∗(1+0.02)20=20,000 * (1 + 0.02) ^ 20 = 29,778.61 Country B = 5,000∗(1+0.08)20=5,000 * (1 + 0.08) ^ 20 = 23,304.79

After 30 years: Country A = 20,000∗(1+0.02)30=20,000 * (1 + 0.02) ^ 30 = 36,398.24 Country B = 5,000∗(1+0.08)30=5,000 * (1 + 0.08) ^ 30 = 50,313.28

After 40 years: Country A = 20,000∗(1+0.02)40=20,000 * (1 + 0.02) ^ 40 = 44,482.48 Country B = 5,000∗(1+0.08)40=5,000 * (1 + 0.08) ^ 40 = 108,366.23

From the calculations, we can see that Country B's real GDP per capita will be greater than Country A's after 30 years. So, the correct answer is "Country B‘s real GDP will be greater than Country A’s real GDP after 30 years".

This problem has been solved

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