The annual rate of growth in population of a town is 10%. If its present population is 33275, what was it 3 years ago?
Let 3 years ago population = P
Present population = 33275
Time, n = 3 years
Increases rate, R = 10% 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
⇒ 33275 = P (1 + 10/100)3
⇒ 33275 = P (1 + 1/10)3
⇒ 33275 = P (11/10)3
⇒ 33275 = P × 1331/1000
⇒ P = 33275 × 1000/1331
⇒ P = 25 × 1000
⇒ P = 25000
∴ 3 years ago population is 25000.