# Compound Interest

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You might have come across statements like “one year interest for FD (fixed deposit) in the bank @ 9% per annum” or ‘Savings account with interest @ 5% per annum’.

**Interest** is the extra money paid by institutions like banks or post offices on money deposited (kept) with them. Interest is also paid by people when they borrow money. We already know how to calculate

**Example 7:** A sum of ₹ 10,000 is borrowed at a rate of interest 15% per annum for 2 years. Find the simple interest on this sum and the amount to be paid at the end of 2 years.

**Solution:**

- On ₹ 100, interest charged for 1 year is ₹ 15.
- For ₹ 10,000: interest charged = 15/100 × 10000 = ₹
- Interest for 2 years = ₹ 1500 × 2 = ₹
- Amount to be paid at the end of 2 years = Principal
+ Interest = ₹ - Amount to be paid at the end of 2 years has been found.

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Normally, the interest paid or charged is never simple. The interest is calculated on the amount of the previous year. This is known as interest compounded or

**Person1**: My father has kept some money in the post office for 3 years. Every year the money increases as more than the previous year.

**Person2**:We have some money in the bank. Every year some interest is added to it, which is shown in the passbook. This interest is not the same, each year it increases.

**Person3**:Normally, the interest paid or charged is never simple. The interest is calculated on the amount of the previous year. This is known as interest compounded or Compound Interest (C.I.).

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Let us take an example and find the interest year by year. Each year our sum or principal changes.

**Calculating Compound Interest**

A sum of ₹ 20,000 is borrowed by Heena for 2 years at an interest of 8% compounded annually. Find the **Compound Interest (C.I.)** and the amount she has to pay at the end of 2 years.

Aslam asked the teacher whether this means that they should find the interest year by year. The teacher said ‘yes’, and asked him to use the following steps :

Find the

**Simple Interest (S.I.)**for one year.Let the principal for the first year be P

_{1}.Here, P_{1}= ₹ 20,000SI

_{1}= SI at 8% p.a. for 1st year = ₹ = ₹20000 × 8 100

2. Then find the amount which will be paid or received. This becomes principal for the next year.

Amount at the end of 1st year = P_{1} + SI_{1} = ₹ 20000 + ₹ 1600 = ₹ _{2} (Principal for 2nd year)

3. Again find the interest on this sum for another year.

SI_{2} = SI at 8% p.a.for 2nd year = ₹

4. Find the amount which has to be paid or received at the end of second year.

Amount at the end of 2nd year = P_{2} + SI_{2}= ₹ 21600 + ₹ 1728 = ₹

Total interest given = ₹ 1600 + ₹ 1728 = ₹

Reeta asked whether the amount would be different for simple interest. The teacher told her to find the interest for two years and see for herself.

SI for 2 years = ₹

Reeta said that when compound interest was used Heena would pay ₹ 128 more.

Let us look at the difference between simple interest and compound interest. We start with ₹ 100. Try completing the chart.

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## Quiz

Note that in 3 years, Interest earned by Simple Interest = ₹ (130 – 100) = ₹

Interest earned by Compound Interest = ₹ (133.10 – 100) = ₹

Note: The Principal remains the