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# What is meant by Compounding?

Compounding is a process of calculating interesting rates. Unlike simple interest rates where interest rates remain the same over a period, in the case of compound interest, the interest rate goes on increasing with passing time. In the case of compounding, therefore, the wealth grows at a faster rate than in the case of simple interest.

For example, a person who has invested INR 100 in a project where the interest rate is 10% would get INR 110 at the end of the first year. At the end of the second year, he should get returns for the amount of INR 110,not 100. Therefore, the extra INR 10 would also be calculated as a base for incurring returns. The person should now get INR 121 including the interest of the INR 10 for the second year. This is called compounding.

**Note** − *Compounding is a process of calculating interest rates by including the earned interests into account as further investments*.

## Compound Interest and Simple Interest

Compounding is a process of finding the future value of cash flow by including the application of compound interest. In compound interest, the interest grows automatically including the interest on the earned interest amount. In a simple interest rate, the interest rate is calculated only on the principal or original amount.

**Note** − *Simple interest remains the same over a period of time and is easier to calculate. However, it is not used by most financial authorities.*

## Calculating the Value of Investment with Compound Interest

Let **F** be the amount of total wealth including the interest rate.

So, for the first year,

**F1 = P + P × i = P (1+i)**

**F2 = F1 + F1i = F1 (F1 + i) = P (1+i) (1+i) = P(1+i) ^{2}**

Similarly,

**F3 = P (1+i)**^{3}

So, for principal P and future sum F, and interest rate (i), and n years, the compounded value is given by,

**Fn = P(1+i) ^{n}**

The term **(1+i) ^{n}** is known as the compound value factor of lump-sum 1. It is always greater than 1 for positive

**i**which means that CVF goes up with increasing

**i**and

**n**.

**Note** − *The future sum of an investment would always go up due to the positive compound factor. For a given sum of investment, it will go up depending on the length of investment and interest rates*.

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