#### notes

There are some situations where we could use the formula for calculation of amount in CI. Here are a few.

(i) Increase (or decrease) in population.

(ii) The growth of a bacteria if the rate of growth is known.

(iii) The value of an item, if its price increases or decreases in the intermediate years.**Example:** 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.**Solution:** 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 beginning of 1998 = 20000 (we treat this as the principal for the 1st year)

Increase at 5% = `5/100 xx 20000 = 1000`

Population in 1999 = 20000 + 1000 = 21000 .....(Treat as the principal for the 2nd year.)

Increase at 5% = `5/100 xx 21000 = 1050`

Population in 2000 = 21000 + 1050

= 22050 .....( Treat as the principal for the 3nd year.)

Increase at 5% = `5/100 xx 22050`

=1102.5

At the end of 2000 the population = 22050 + 1102.5 = 23152.5

or, Population at the end of 2000 = 20000 `(1+5/100)^3`

`= 20000 xx 21/20 xx 21/20 xx 21/20`

= 23152.5

So, the estimated population = 23153.