#### Question

The population of a suburb is 16000. Find the rate of increase in the population if the population after two years is 17640.

#### Solution

Here, P = Population of a suburb = 16000

A = Population after two years =17640

R = R %

N = 2 years

A = P `(1 + "R"/100)^"N"`

= 17640 = 16000 `(1 + "R"/100)^2`

= `17640/16000` = `(1 + "R"/100)^2`

= `441/400` = `(1 + "R"/100)^2`

= `(21/20)^2` = `(1 + "R"/100)^2`

= `1 + "R"/100` = `21/20`

= `"R"/100 = 21/20 - 1`

= `"R"/100 = 1/20`

= R = 5

Hence, the rate of increase in the population is 5 p.c.p.a.

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Solution The Population of a Suburb is 16000. Find the Rate of Increase in the Population If the Population After Two Years is 17640. Concept: Application of Formula for Compound Interest.