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In a developing country, the growth rate of capital is 9% per hour of work, and the growth rate of technology is 6%. If population growth is 6% per year, use the Rule of 72 to estimate how many years it will take for the developing country's income per capita to double.  years

Question

In a developing country, the growth rate of capital is 9% per hour of work, and the growth rate of technology is 6%. If population growth is 6% per year, use the Rule of 72 to estimate how many years it will take for the developing country's income per capita to double.  years

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Solution

The Rule of 72 is a simple way to determine how long an investment will take to double given a fixed annual rate of interest. By dividing 72 by the annual rate of return, investors obtain a rough estimate of how many years it will take for the initial investment to duplicate itself.

In this case, we are looking at the growth rate of capital and technology, which are 9% and 6% respectively. However, we also need to consider the population growth rate, which is 6%.

The net growth rate can be calculated as follows:

Net growth rate = Growth rate of capital + Growth rate of technology - Population growth rate Net growth rate = 9% + 6% - 6% = 9%

Now, we can use the Rule of 72 to estimate how many years it will take for the income per capita to double.

Years to double = 72 / Net growth rate Years to double = 72 / 9 = 8 years

So, it will take approximately 8 years for the developing country's income per capita to double, assuming the growth rates remain constant.

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