Discussion
The population of a city increases at the rate of 4% p.a. but there is an additional annual increase of 1% in the population due to some job seekers. The percentage increase in the population after 2 years is?
Answer: C
The two sources of growth act in the same year, so combine them into a single annual rate.
\[ 4\% + 1\% = 5\% \text{ per annum} \]
Population growth compounds, so over two years:
\[ (1.05)^{2} = 1.1025 \]
\[ \text{increase} = 10.25\% \]
Simply doubling the 5% would give 10%; the extra 0.25% is the second year's growth on the first year's addition.
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