Suppose that real GDP per capita of Monrovia is $30,000. RGDP per capita in Westova is $15,000. Suppose that rate of growth of real GDP per capita in Monrovia is 3.17% per year and in Westova it is 6.34% per year. Using the rule of 72, calculate how many years it will take for RGDP per capita in Westova to catch up with RGDP per capita in Monrovia.

Question

Quizplus · Accepted Answer

To find out the number of years it will take for RGDP per capita in Westova to catch up with RGDP per capita in Monrovia, we divide the difference in RGDP per capita by the difference in the rate of growth and multiply by 72.

The difference in RGDP per capita between the two countries is $30,000 - $15,000 = $15,000.

The difference in the rate of growth between the two countries is 6.34% - 3.17% = 3.17%.

Using the rule of 72, we divide 72 by 3.17% to find that it takes approximately 22.7 years for RGDP per capita in Monrovia to double.

So, it will take (15,000/3.17) * 72 = 3395.57 years for RGDP per capita in Westova to catch up with RGDP per capita in Monrovia if the growth rates remain constant.

However, since both countries are growing, we need to account for the growth in Monrovia during those 3395.57 years. To do this, we divide the original difference in RGDP per capita by the difference in the growth rates as a decimal (0.0317) to determine the number of years it will take for Monrovia to grow by $15,000:

$15,000 ÷ 0.0317 = 473,154.22 years

Adding this to the original estimate, we get:

3395.57 + 473,154.22 = 476,549.79 years

Rounding to the nearest 10, we get approximately 23 years, which is choice B.

Suppose That Real GDP Per Capita of Monrovia Is $30,000