Question:
The population of a town is 125000. It is increasing at the rate of 2% per annum. What will be its population after 3 years?
Solution:
Population of the town, $P=125000$
Rate of increase, $R=2 \%$
Time, $n=3$ years
Then the population of the town after 3 years is given by
Population $=P \times\left(1+\frac{R}{100}\right)^{3}$
$=125000 \times\left(1+\frac{2}{100}\right)^{3}$
$=125000 \times\left(\frac{100+2}{100}\right)^{3}$
$=125000 \times\left(\frac{102}{100}\right)^{3}$
$=125000 \times\left(\frac{51}{50}\right)^{3}$
$=125000 \times\left(\frac{51}{50}\right) \times\left(\frac{51}{50}\right) \times\left(\frac{51}{50}\right)$
$=(51 \times 51 \times 51)$
$=132651$
Therefore, the population of the town after three years is 132651 .