# Compound Interest

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 ₹
. - For ₹ 10,000: interest charged =
×15 100 = ₹ - Interest for 2 years = ₹ 1500 ×
= ₹ - 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.

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)

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 :

**(1) Find the Simple Interest (S.I.) for one year**.

Let the principal for the first year be

**(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 =

**(3) Again find the interest on this sum for another 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 =

Total interest given = ₹

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.

## Quiz

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

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

**Note:** The Principal remains the