The population of a town is 125000.

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 .

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