# Deducing a Formula for Compound Interest

Zubeda asked her teacher, ‘Is there an easier way to find compound interest?’ The teacher said ‘There is a shorter way of finding compound interest. Let us try to find it.’

**Suppose **.

Let

(1) = ₹

So,

= ₹ 5000

(2) = ₹ 5000

= ₹

₹ 5000

=

=

=

Proceeding in this way the amount at the end of *n* years will be

A = P

So, Zubeda said, but using this **we get only the formula for the amount to be paid at the end of n years, and not the formula for compound interest**.

Aruna at once said that we know **CI = A – P**, so we can easily find the compound interest too.

**Example 8: Find CI on ₹ 12600 for 2 years at 10% per annum compounded annually**.

**Solution:** We have

A = P

₹ 12600

₹ 12600

CI = A - P = ₹

### TRY THESE

**Find CI on a sum of Rs. 8000 for 2 years at 5% per annum compounded annually**.

To find the compound interest (CI) on a sum, we can use the formula:

**CI = P × - **

Where: P is the **principal amount** (Rs. **rate of interest** (**time period** (

First, calculate the amount after 2 years using the formula:

**A = P × ** =

= 8000 ×

Now, find the compound interest:

**CI = A − P** =

**So, the compound interest on Rs. 8000 for 2 years at 5% per annum is Rs. 820**.