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Chapter 7: Problem 33

An economy starts off with a GDP per capita of 12,000 euros. How large will the GDP per capita be if it grows at an annual rate of \(3 \%\) for 10 years? \(3 \%\) for 30 years? \(6 \%\) for 30 years?

Short Answer

Expert verified
After 10 years with a 3% annual growth rate, the GDP per capita will be approximately 16,386.16 euros. After 30 years with a 3% annual growth rate, the GDP per capita will be approximately 29,456.42 euros. Finally, after 30 years with a 6% annual growth rate, the GDP per capita will be approximately 68,212.23 euros.

Step by step solution

01

To calculate the GDP per capita after a specific number of years, we will use the compound interest formula given by \(Future\ GDP\ Per\ Capita = Current\ GDP\ Per\ Capita * (1 + Annual\ Growth\ Rate)^{Number\ of\ Years}\). #2: Calculate the GDP per capita after 10 years with 3% annual growth:

Using the above formula and given values, we will calculate the GDP per capita after 10 years with a 3% annual growth rate. \(Future\ GDP\ Per\ Capita = 12,000 * (1 + 0.03)^{10}\) \(Future\ GDP\ Per\ Capita = 12,000 * (1.03)^{10}\) \(Future\ GDP\ Per\ Capita \approx 16,386.16\) After 10 years with a 3% annual growth rate, the GDP per capita will be approximately 16,386.16 euros. #3: Calculate the GDP per capita after 30 years with 3% annual growth:
02

We will now calculate the GDP per capita after 30 years with a 3% annual growth rate. \(Future\ GDP\ Per\ Capita = 12,000 * (1 + 0.03)^{30}\) \(Future\ GDP\ Per\ Capita = 12,000 * (1.03)^{30}\) \(Future\ GDP\ Per\ Capita \approx 29,456.42\) After 30 years with a 3% annual growth rate, the GDP per capita will be approximately 29,456.42 euros. #4: Calculate the GDP per capita after 30 years with 6% annual growth:

Lastly, we will calculate the GDP per capita after 30 years with a 6% annual growth rate. \(Future\ GDP\ Per\ Capita = 12,000 * (1 + 0.06)^{30}\) \(Future\ GDP\ Per\ Capita = 12,000 * (1.06)^{30}\) \(Future\ GDP\ Per\ Capita \approx 68,212.23\) After 30 years with a 6% annual growth rate, the GDP per capita will be approximately 68,212.23 euros.

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