Question

The population of a town increases at a certain rate per annum. The present population of the town is 3600. If the population after 5 years is 4800, then find the population after 10 years?

• A. 5000
• B. 6000
• C. 6400
• D. 7000

Answer 1

The correct option is C 6400

Let the rate of increase in population be r % per annum.

We can find the population after 't' years by using the concept of compound interest.

By using the formula for compound interest, the amount after 't' years can be calculated by the formula

$A=P\times (1+\frac{R}{100}{)}^t$

Similarly, population after 't' years can be calculated by the formula

$F=I(1+\frac{R}{100}{)}^t$

where F is the population after 't' years, I is the initial population and R is the rate of increase in population.

Given, the initial population is 3600 and the population after 5 years is 4800.

So,
$4800=3600{(1+\frac{r}{100})}^5$

$\Rightarrow {(1+\frac{r}{100})}^5=\frac{4800}{3600}\Rightarrow {(1+\frac{r}{100})}^5=\frac{4}{3}$

The population after 10 years is given by
$F=3600{(1+\frac{r}{100})}^{10}$
$F=3600({(1+\frac{r}{100})}^5{)}^2$
$F=3600(\frac{4}{3}{)}^2$
$F=6400$