The annual rate of growth in population of a town is 5%. If its present population is 4000, what will be its population after 2 years?
Population of a town, P = 4000
Time, n = 2 years
Increasing rate, R = 5% per annum
Now,
Amount (A) = P (1 + R/100)n [Where, A = Amount with compound interest
P = Present value
R = Annual interest rate
n = Time in years]
∴ Population = P (1 + R/100)n
= 4000 (1 + 5/100)2
= 4000 (1 + 1/20)2
= 4000 (21/20)2
= 4000 × 21/20 × 21/20
= 200 × 21 × 21/20
= 10 × 21 × 21
= 4410
∴ Population of a town after 2 years is 4410.