Question

This question is an application of Rule of 72. Consider a country for which GDP per capital doubles every 50 years. Calculate the annual growth rate for this country. Consider another country for which GDP per capita doubles every 25 years. Calculate the annual growth rate for the second country. Given everything else constant, calculate in how many years catch up effect will occur between the two countries when initially, the first country’s GDP per capita is 4 times that of the second country? Explain your answer

Answer 1

According to rule of 72,

Doubling period = 72 / Interest rate

=> Interest rate =72 /Doubling period.

1. In first case the GDP doubles in 50 years

Interest rate = 72 / 50 = 1.44%

2. In second case the GDP doubles in 25 years.

Interest rate = 72 / 25 = 2.88%

3. First country's GDP is 4 times the GDP of second country.

Assume the GDP of country B = x

Thus, the GDP of country A =.4x

Let us assume in n years the GDP of both countries will be equal.

After n years the GDP of country A = 4x×1.0144^n

GDP of country B = x × 1.0288^n

Equate these two values we get

Approximately, in 98 years the GDP of two countries will be equal.

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