The population of village is $5000$ and it increased at the rate of $2\%$ every year after 2 years the population will be

Population of village compounding  yearly

$P=5000,R=2\%,n=2$

After 2 years population is

$=P{\left(1+\frac{R}{100}\right)}^n=5000{\left(1+\frac{2}{100}\right)}^2$

$=5000\times \frac{102}{100}\times \frac{102}{100}$

$=\frac{102\times 102}{2}=51\times 102$

$=5202$