Question

Country A starts with real GDP per capita equal to $40,000 and Country B starts with real GDP per capita equal to $2,000.

Today the RGDP per capita in A is ___ times the value in B.

Country A is growing at a rate of 3.5% per year and Country B is growing at a rate of 7% per year. Assume these growth rates do not change.

Country A will double its RGDP per capita in _____ years and country B will double its RGDP per capita in _____ years.

Enter whole numbers.

In 20 years real GDP per capita in Country A will be $__

In 40 years real GDP per capita in Country A will be $__

In 60 years real GDP per capita in Country A will be $ __

In 20 years real GDP per capita in Country B will be $ __

In 40 years real GDP per capita in Country B will be $ __

In 60 years real GDP per capita in Country B will be $ __

After 60 years RGDP per capita in A is _______ times the value in B.   Round to two decimal places.

Answer 1

Country A real GDP per capita = $40000

Country B real GDP per capita = $2000

RGDP per capita in A is 20 times the value in B.

i.e., ($40000 / $2000) = 20

According to Rule 70:

Number of years to double = (70 / Annual growth rate).

Country A is growing at a rate of 3.5% per year.

Number of years to double = (70 / 3.5) = 20.

Hence, Country A will double its RGDP per capita in 20 years.

Country B is growing at a rate of 7% per year.

Number of years to double = (70/7) = 10

Hence, Country B will double its RGDP per capita in 10 years.

In every 20 years, Country A RGDP per capita will get double.

In 20 years real GDP per capita in Country A will be $80,000 (i.e., $40000 * 2 = $80000)

In 40 years real GDP per capita in Country A will be $160000 (i.e., $40000 * 2 *2 = $160000)

In 60 years real GDP per capita in Country A will be $320,000 (i.e., $40000 * 2*2*2 = $320000)

In every 10 years, Country B RGDP per capita will get double.

So, in every 20 years, it will increase by 4 times

In 20 years real GDP per capita in Country B will be $8000 (i.e., $2000 * 4= $8000)

In 40 years real GDP per capita in Country B will be $32000 (i.e., $2000 * 4 * 4= $32000)

In 60 years real GDP per capita in Country B will be $128000 (i.e., $2000 * 4*4*4= $128000)

After 60 years, RGDP per capita in Country A will be $320000 and in Country B will be $128000.

After 60 years RGDP per capita in A is 2.5 times the value in B.

i.e., ($320000 / $128000) = 2.5