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# Applications of Compound Interest Formula

#### 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.

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