# Deducing a Formula for Compound Interest

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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. | or | ||

So, | or | ||

= ₹ 5000 | |||

2. | or | ||

= ₹ | |||

₹ 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.

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

**Solution:** We have,

A = P

where Principal (P) = ₹ 12600, Rate (R) = 10, Number of years (n) = 2

₹ 12600

₹ 12600

CI = A - P = ₹15246 - ₹ 12600 =