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In compound interest, if the interest earned in a period is not paid back to the lender, then the interest is added to the sum lent, and the amount thus obtained becomes the principal for the next period.

The difference of the final amount and the original amount is called Compound Interest (C.I.).

$Compound \ Interest = Final \ Amount - Original \ Principal = A - P$

The time period after which the Principal changes is called conversion period.

For example:

• If the interest is compounded annually, then the principal changes annually or every year.
• If the interest is compounded every six months, then the principal increases every six months.

Note: In case of Simple Interest, the principal stays the same through out the term. While in case of compound interest, the principal changes based on the period mentioned in the terms of the loan.

Also note:

For the same sum and the same rate of interest compounded annually

•  $C.I. \ of \ 3^{rd} \ Year > C.I. \ of \ 2^{nd} \ Year > C.I. \ of \ 1^{st} \ Year$

Similarly, if the same sum and the same rate of interest compounded half yearly

• $C.I. \ of \ 3^{rd} \ Half \ Year > C.I. \ of \ 2^{nd} \ Half \ Year > C.I. \ of \ 1^{st} \ Half \ Year$

Also the difference between the C.I. for any two consecutive conversion periods is the interest of one period on the C.I. of the preceding period.

• For example: If $1000 \ Rs.$ and $1050 \ Rs.$ are the C.I. of two consecutive years, then the difference $1050 \ Rs. - 1000 \ Rs = 50 \ Rs$ is the interest of one year on $1000 \ Rs.$

Similarly, the difference between the Amounts of two consecutive conversion periods  is the interest of one period on the amount of the preceding period.

• For example: If $1000 \ Rs.$ and $1100 \ Rs$ are amounts of two consecutive periods, then $100 \ Rs.$is the interest on $1000 \ Rs.$

Important Results that you should be aware of:

1. If the C.I. of 1st Period is $x \ Rs.$, then the C.I. for the next period on the same sum and at the same rate = $x \ Rs.$ + Interest for one period on $x \ Rs.$.
2. Similarly, if the amount at C.I. in a particular period is $y \ Rs.$., then the amount for the next period, on the same sum and the same rate = $y \ Rs.$ +Interest on $y \ Rs.$ for one period.