Question

There is a continuous growth in population of a village at the rate of $5\%$ per annum. If its present population is 9261, what it was 3 years ago?

Answer 1

Let 3 years ago, population = P
Present population = 9261
Rate of increase (R) $5\%$ p.a
Period (n) = 3 years
$\because A=P{(1+\frac{R}{100})}^n$
$\Rightarrow 9261=P{(1+\frac{5}{100})}^3=P{\left(\frac{21}{20}\right)}^3$
$\therefore P=9261÷{\left(\frac{21}{20}\right)}^3=9261\times {\left(\frac{20}{21}\right)}^3$
$=9261\times \frac{20}{21}\times \frac{20}{21}\times \frac{20}{21}=8000$
$\therefore$ 3 years ago, population = 8000