Question

Three years ago, the population of a town was 50000. If the annual increase during three successive years be at the rate of 4%, 5% and 3% respectively, find the present population.

Answer 1

$$\begin{gathered} \mathrm{Here}, \\ \mathrm{P}=\mathrm{Initial}\mathrm{population}=50,000 \\ {\mathrm{R}}_1=4\% \\ {\mathrm{R}}_2=5\% \\ {\mathrm{R}}_3=3\% \\ \mathrm{n}=\mathrm{Number}\mathrm{of}\mathrm{years}=3 \\ \therefore \mathrm{Population}\mathrm{after}\mathrm{three}\mathrm{years}=\mathrm{P}\left(1+\frac{{\mathrm{R}}_1}{100}\right)\left(1+\frac{{\mathrm{R}}_2}{100}\right)\left(1+\frac{{\mathrm{R}}_3}{100}\right) \\ =50,000\left(1+\frac{4}{100}\right)\left(1+\frac{5}{100}\right)\left(1+\frac{3}{100}\right) \\ =50,000\left(1.04\right)\left(1.05\right)\left(1.03\right) \\ =56,238 \\ \mathrm{Hence},\mathrm{the}\mathrm{population}\mathrm{after}\mathrm{three}\mathrm{years}\mathrm{is}56,238. \end{gathered}$$