Question

GDP per Capita Growth and Rule of 72

	Current Year	Previous Year	Growth Rate
Real GDP	$8.4 trillion	$8.0 trillion
Population	202 million	200 million
GDP per Capita	$	$

Formulas you could use:

• Growth Rate in percentage = (Current year value – previous year value)/ previous year
• GDP per Capita = Real GDP/population (Ch6 Section 6.4)
• Future value = Present value x (1 + growth rate)^number of years (Ch7 Section 7.2)
• Rule of 72:
• 72/growth rate = number of years to double the actual value (Ch19 Section19.2)

The table above is the data for country D, a developed country.

1. Calculate the annual growth rate of Real GDP for country D.
2. Calculate the annual growth rate of population.
3. Calculate GDP per Capita for the current year and previous year.
4. What is the annual growth rate of GDP per Capita? How do you find it?
5. Using your calculated figure in (4), calculate the amount of GDP per capita (future value) after 18 years.
6. Using the rule of 72, calculate how many years GDP per capita will be double.

Answer 1

(1)

Annual growth rate, real GDP = (8.4 / 8) - 1 = 1.05 - 1 = 0.05 = 5%

(2)

Annual growth rate, population = (202 / 200) - 1 = 1.01 - 1 = 0.01 = 1%

(3)

GDP per capita = Real GDP / Population

Previous year = (8 x 1,000 x 1,000 million) / 200 million = $40,000

Current year = (8.4 x 1,000 x 1,000 million) / 202 million = $41,584.16

(4)

Annual growth rate, GDP per capita = (41,584.16 / 40,000) - 1 = 1.0396 - 1 = 0.0396 = 3.96%

(5)

GDP per capita after 18 years ($) = 41,584.16 x (1.0396)¹⁸ = 41,584.16 x 2.0118 = 83,660.57

(6)

Doubling period = 72 / Growth rate of GDP per capita = 72 / 3.96 = 18.18 years