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.
Solution:
Here,
$\mathrm{P}=$ Initial population $=50,000$
$\mathrm{R}_{1}=4 \%$
$\mathrm{R}_{2}=5 \%$
$\mathrm{R}_{3}=3 \%$
$\mathrm{n}=$ Number of years $=3$
$\therefore$ Population after three years $=\mathrm{P}\left(1+\frac{\mathrm{R}_{1}}{100}\right)\left(1+\frac{\mathrm{R}_{2}}{100}\right)\left(1+\frac{\mathrm{R}_{3}}{100}\right)$
$=50,000\left(1+\frac{4}{100}\right)\left(1+\frac{5}{100}\right)\left(1+\frac{3}{100}\right)$
$=50,000(1.04)(1.05)(1.03)$
$=56,238$
Hence, the population after three years is 56,238 .