Question

The population of a city was 20,000 in the year 1997. It increased at the rate of 5% p.a. Find the population at the end of the year 2000.

Answer 1

There is 5% increase in population every year, so every new year has new population.

Thus, we can say it is increasing in compounded form.

Population in the year1997 = 20,000 (we treat this as the principal for the 1st year)

Increase at 5% = $\frac{5}{100}$ × 20000 = 1000

Population in the year1998 = 20000 + 1000 = 21000

Increase at 5% = $\frac{5}{100}$ × 21000 = 1050

Population in the year 1999 = 21000 + 1050 = 22050

Increase at 5% = $\frac{5}{100}$ × 22050 = 1102.5

At the end of the year 2000 the population = 22050 + 1102.5 = 23152.5
or
Population at the end of the year 2000 = 2000 × ${[1+\frac{5}{100}]}^3$

= 20000 × $\frac{21}{20}$ × $\frac{21}{20}$ × $\frac{21}{20}$

= 23152.5

So,the estimated population = 23153