The population of a village increases at the rate of $ 5 \% $ p.a. If its present population is $ 18,000, $ what will be its value after 2 years?

Given:

The annual rate of growth in the population of a village is 5%.

The present population of the village is 18000.   

To do:

We have to find the population of the village after 2 years. 

Solution:

Let the population of the village 2 years be $x$.

This implies,

$x=18000(1+\frac{5}{100})^2$

$x=18000\times(\frac{105}{100})^2$

$x=18000\times(\frac{21}{20})^2$

$x=\frac{18000}{400}\times441$

$x=45\times441$

$x=19845$

The population of the village after 2 years is 19845.