# Applications of Compound Interest Formula:

There are some situations where we could use the formula for calculation of amount in CI. Here are a few.
1. Increase (or decrease) in population.
2. The growth of bacteria if the rate of growth is known.
3. 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.

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

Population in the beginning of 1998 = 20000
Increase at 5% = 5/100 × 20000 = 1000
Population in 1999 = 20000 + 1000 = 21000

Increase at 5% = 5/100 × 21000 = 1050
Population in 2000 = 21000 + 1050 = 22050

Increase at 5% = 5/100 × 22050 = 1102.5
At the end of 2000 the population = 22050 + 1102.5 = 23152.5

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.

#### Example

A TV was bought at a price of ₹ 21,000. After one year the value of the TV was depreciated by 5% (Depreciation means reduction of value due to use and age of
the item). Find the value of the TV after one year.
Principal = ₹ 21,000
Reduction = 5% of ₹ 21000 per year
= ₹ (21000 xx 5 xx 1)/100
= ₹ 1050
Value at the end of 1 year = ₹ 21000 - ₹ 1050 = ₹ 19,950.

Value at the end of 1 year =  ₹ 21000(1 - 5/100)

= ₹ 21000 xx 19/20

= ₹ 19,950.

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