# Simple and Compound Interest

When you borrow money, you have to return the amount within a specific period, along with some extra money. This extra money is called **Interest**. The rate at which the interest is calculated on the principal is called Rate of Interest.

There are two types of interests - simple and compound.

**Simple Interest:** The amount charged by the lender for giving you his money for a specific amount of time.

**Compound Interest:** Here, the lender calculates the interest on interest.

### Simple Interest

When money is borrowed at simple interest, the interest charged is same irrespective of the period involved.

SI = (P*R*T)/100, where

- SI = Simple Interest
- P = Principle (the actual money borrowed)
- T =Time in Years
- R = Rate of interest (% per year)

Amount paid to the lender is interest and principle amount.

Amount, A = P + I = P(1+RT/100)

### Compound Interest

In compound interest, the interest is added to the principal at the end of each period and the amount thus obtained becomes the principal for the next period. The process is repeated till the end of the specified time.

When the interest is compounded annually, amount after n years

A = P(1 + R/100)^{n}

CI = A - P

When the principal changes every year, we say that the interest is compounded annually.

When the principal changes as per every six months, we say that the interest is compounded half yearly or semi-annually. In this case, the formula changes. n becomes 2n and R becomes R/2.

When the principal changes every three months, we say that the interest is compounded quarterly. Similarly, when the principal changes after every month, we say that the interest is compounded monthly.

### SI and CI

The difference between the simple interest and compound interest for 2 year (or terms) is given by:

D = P(R/100)^{2}