# Applications of Compound Interest Formula

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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 9:** 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:**

- Increase at 5% =
5 100 × 20000 = - Population in 1999 = 20000 + 1000 =
(Treat as the Principal for the 2nd year ) - Population in 2000 = 21000 + 1050 =
(Treat as the Principal for the 3rd year ) - At the end of 2000 the population = 22050 + 1102.5 =

So, at the end of the year 2000, the population is approximately =

Aruna asked what is to be done if there is a decrease. The teacher then considered the following example.

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**Example 10:** A TV was bought at a price of Rs. 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.

**Solution:**

- TV was bought at a price of Rs. 21,000.
- Reduction = 5% of ₹ 21000 per year
- Hence reduction = ₹
- Value at the end of 1 year = ₹ 21000 – ₹ 1050 = ₹
- We have found the answer.