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Singapore​'s real GDP was 188 billion dollars in 2005 and 196 billion dollars in 2006. The population was 4.4 million in 2005 and 4.5 million in 2006. Calculate Singapore​'s economic growth rate in 2006​, the growth rate of real GDP per person in 2006​, and the approximate number of years it will take for real GDP per person in Singapore to double if the 2006 economic growth and population growth rates are maintained.

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Answer:

* Singapore​'s economic growth rate in 2006: 4.26%

* Growth rate of real GDP per person in 2006: 1.94%

* The approximate number of years it will take for real GDP per person in Singapore to double if the 2006 economic growth and population growth rates are maintained: 36 years

Explanation:

* Singapore​'s economic growth rate in 2006: Real GDP in 2006/ Real GDP in 2005 -1 = 196/188 -1 = 4.26%;

* Growth rate of real GDP per person in 2006:

+ Real GDP per person in 2005: 188 billion/4.4 million = $42,727.3

+ Real GDP per person in 2006: 196 billion/4.5 million = $43,555.6

+ Growth rate of real GDP per person in 2006 = 43,555.6/42,727.3 -1 = 1.94%

* The approximate number of years it will take for real GDP per person in Singapore to double if the 2006 economic growth and population growth rates are maintained:

Denote x is the number of years need to be found

Population growth rate in 2006: 4.5/4.4 -1 = 2.27%

The expected GDP per person after x years : 43,555.6 x 2 = $87,111

The expected GDP per person = Real GDP after x years / Population after x years = 87,111

<=>  196,000 x 1.0426^x / 4.5 x 1.0227^x = 87,111 ( unit is million)

<=> 1.0426^x / 1.0227^x  = 1.99 <=> x = 36 years

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