Multiple choice

The population of an island is 27,000 and its national income is Rs. 52,65,000. It is forecasted that the population will increase at a compounded annual growth rate of 10% and the national income at 7%. Considering that this will go on for a period of five years, what will be the percentage of change in the per capita income of the island?

  1. Decrease by 12.913%

  2. Increase by 12.913%

  3. Increase of 13.913%

  4. Decrease of 14.913%

  5. Increase of 15.913%
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A Correct answer
Explanation

Initial per capita = 5265000 / 27000 = 195. After 5 years: Income = 5265000 * (1.07)^5 = 7382226. Population = 27000 * (1.1)^5 = 43516. New per capita = 7382226 / 43516 = 169.64. Change = (169.64 - 195) / 195 = -12.913%.

AI explanation

Per capita income is national income divided by population, so the ratio of new per capita income to the old one over 5 years is (1.07^5) / (1.10^5) = (1.07 / 1.10)^5. Calculating this ratio, (0.9727)^5 is approximately 0.87087. Since this is less than 1, it represents a decrease of (1 - 0.87087) * 100 = 12.913%.

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