Final answer:
We determine the future GDP per capita given an initial value and a yearly growth rate, using the formula for compound interest. The calculations show increases to 16,119.41 euros in 10 years at 3%, 29,202.94 euros in 30 years at 3%, and 68,843.05 euros in 30 years at 6%, illustrating significant potential growth for the European Union over time.
Step-by-step explanation:
The question concerns calculating the growth of GDP per capita over a certain period, given an annual growth rate. To determine the new GDP per capita after growth, we apply the formula for compound interest: GDPt = GDP0 × (1 + r)t, where GDPt is the future value of GDP per capita, GDP0 is the initial GDP per capita, r is the annual growth rate, and t is the time in years.
Calculating Growth Over Different Time Periods
Starting with a GDP per capita of 12,000 euros:
- At an annual growth rate of 3% for 10 years, the formula gives us GDP10 = 12,000 × (1 + 0.03)10. After calculation, it approximately equals 16,119.41 euros.
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- At the same annual growth rate of 3% for 30 years, we use GDP30 = 12,000 × (1 + 0.03)30. This equals around 29,202.94 euros after calculation.
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- For a higher annual growth rate of 6% for 30 years, the calculation is GDP30 = 12,000 × (1 + 0.06)30, resulting in about 68,843.05 euros.
The European Union has shown that with consistent growth, economies can expand significantly over time, contributing to the overall prosperity of the region. This resonates with the historical data presented showing that European countries are a considerable force within the global economy despite the comparative smallness of their geographic size.
It is also noteworthy that the average GDP growth rate per capita in leading industrialized countries has been around 2% per year, putting these growth rates into perspective. Considering that the EU's mission includes promoting peace and solidarity, economic growth is crucial in supporting political stability and overall development of the Union's member countries.