Question

The population of a village is 1,20,000. If the population increases by 5% every year, what will it be after 3 years?

Answer 1

Population of the village, P = 1, 20,000
Rate of increase in population (R) = 5% p.a.
Number of years (N) = 3 years
Population after three years $=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}}$
$$\begin{gathered} =120000{\left(1+\frac{5}{100}\right)}^3 \\ =120000{\left(1+\frac{1}{20}\right)}^3 \\ =120000{\left(\frac{21}{20}\right)}^3 \\ =120000\times \frac{21}{20}\times \frac{21}{20}\times \frac{21}{20} \\ =138915 \end{gathered}$$