A city’s population increases by 2·5% every year, while migration reduces it by 0·5% each year. What is the overall percentage increase in population after two years ?
4·04%
Net yearly growth rate \(= 2.5\% - 0.5\% = 2\%\), compounded for two years.
Population factor after two years \(= (1 + \frac{2}{100})^{2} = 1.02^{2} = 1.0404\).
Overall increase \(= (1.0404 - 1) \times 100 = 4.04\%\).
Check (successive change formula): \(2 + 2 + \frac{2 \times 2}{100} = 4.04\%\).
Hence, 4·04%.
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