The population of a village is 200,000. If the annual birth rate and the annual death rate are 6% and 3% respectively, then calculate the population of the village after 2 years.
Solution
Correct Answer: Option D
It can be noted that the annual birth rate and the annual death rate both are calculated upon the base population. [For the current year it is 200000]
So we can say, the net annual growth rate = annual birth rate–annualdeath rate
⇒net annual growth rate = 6 – 3 = 3%
⇒The population is increasing at a rate of 3% & the growth is essentially compounded growth.
The formula for annual compound growth is \(A = P \times {\left( {1 + \frac{r}{{100}}} \right)^{n\;}}\)
Where: A = future population; P = initial population; r = annual % growth rate; n = time in years.
Here, P = 200000; r = 3%; n = 2 years.
Putting the values in the above equation \(A = 200000 \times {\left( {1 + \frac{3}{{100}}} \right)^{2\;}}\)
⇒A = 212180
The population of the village after 2 years will be 212180.
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