### Theory:

An immense theoretical physicist Albert Einstein once quoted,

"Compound interest is the eighth wonder of the world.

He who understands it earns it, he who doesn't pays it".

Compound interest is indeed a miracle one. Let us see the exciting story to understand the power of compounding.
Once there was a king, who was a chess enthusiast. He had the habit of challenging the wise person in the game of chess with a reward. One day the sage was challenged by the king, and the sage politely requested that if he won he wanted him to fill the one grain in the first square of the chessboard and double it on the every consequent square. The king accepted the sage's challenge but lost the game. As the king is a man of his words, he ordered his people to execute the sage's wish in the chessboard as:

 $$1$$st square $$1$$ grain $$2$$nd square $$2$$ grains $$3$$rd square $$4$$ grains $$4$$th square $$16$$ grains But on the $$10$$th square, the king has to place $$512$$ grains, on the $$16$$th square $$32786$$ grains, and on the $$20$$th square $$524$$ thousand grains. Now the king acknowledges the difficulties to fulfil the reward. On the last $$64$$th square, the king has to place more than billions of grains, which he could not afford. He especially appreciated the sage's intellect and gave a well-deserved reward.
What an interesting story isn't? Though the story was said in many different ways, the phenomenal concept of exponential compound growth is a constant one.

When calculating compound interest, the number of compounding period (time period), rate of interest and the principle plays a significant role.
Calculating the compound interest
Now, in this chapter, we shall discuss the concept of compound interest and the method of calculating the compound interest and the amount at the end of a particular period. And you will also study the application of compound interest in practical life.

Let's have a quick recall of basics we already studied in the previous classes.

Quick recall:
Interest is the amount of money which is paid for the use of borrowed money.
Example:
Let a person '$$A$$' borrows some money from '$$B$$' for a certain period of fixed time at a fixed rate, then '$$A$$' will pay the borrowed money along with the additional money, which is called interest.
 Basic terms Definition Principal The money borrowed or lend out for a certain period is called the "principal" or the "sum". Amount Amount $$=$$ Principal $$+$$ Interest Time The duration of the period for which the money is borrowed is called the time. Rate Interest per Annum If interest is payable yearly for every $$100$$ rupees, then it is called rate per cent per annum.

Sometimes it so happens that the borrower and the lender agree to fix up a certain unit the of time, say yearly or half-yearly or quarterly to settle the previous account.
In such cases, the amount after the first unit of time becomes the principal for second unit, the amount after the second unit becomes the principal for the third unit and so on.
After the specified period, the difference between the amount and the money borrowed is called the compound interest for the period which is abbreviated as $$C.I$$.

Compound interest $$C.I.$$ $$=$$ Amount $$–$$ Principal