The population of a city was 120000 in the year 2013. During next year it increased by 6% but due to an epidemic it decreased by 5% in the following year. What was its population in the year 2015?
Population of a city in 2013, P = 120000
Time, n = 3 years
Increasing rate, R = 6% 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 of the city in the year 2014,
∴ Population = P (1 + R/100)n
= 120000 (1 + 6/100)1
= 120000 (1 + 3/50)
= 120000 (53/50)
= 120000 × 53/50
= 2400 × 53
= 127200
∴ Population of a city in 2014 is 127200.
Now,
Decreasing rate = 8%
∴Population of the city in the year 2015,
∴ Population = P (1 - R/100)n
= 127200 (1 - 5/100)1
= 127200 (1 - 1/20)
= 127200 (19/20)
= 127200 × 19/20
= 6360 × 19
= 120840
∴ Population of a city in 2015 is 120840.