### Theory:

Interest is the amount of money that is paid for the use of borrowed money.
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.

There are two types of interest:
1. Simple interest
2. Compound interest.
In this chapter, we are going to learn about Simple interest ($$I$$). Before that, we should learn some basic terms deals with interest.
• Principal
• Amount
• Time
Principal $$(P)$$:
The money borrowed or lend out for a certain period is called the "principal" or the "sum".
Amount $$(A)$$:
• The sum of the interest and principal is called the amount.
• $$\text{Amount (A)} =$$ $$\text{Principal (P)} +$$ $$\text{Interest (I)}$$.
Time $$(n)$$:
The duration of the period for which the money is borrowed is called the time.
Rate Interest per Annum $$(r)$$:
If interest is payable yearly for every $$100$$ rupees, then it is called rate per cent per annum. Rate is denoted by $$(r)$$, and rate percentage is denoted by $\frac{r}{100}=r\phantom{\rule{0.147em}{0ex}}%$.

Interest is generally given in per cent for $$1$$ year per annum. Suppose the bank gives an amount of $$₹100$$ at an interest rate of $$₹$$8, it is written as 8$$\%$$ per year or per annum or in short 8$$\%$$ p.a. (per annum).

It means on every $$₹100$$ borrowed, $$₹$$8 is the required interest to be paid for every one year.
Example:
Vijay takes a loan of $$₹$$20000 at 3$$\%$$ per year as the rate of interest. Let us find the amount he has to pay at the end of $$1$$ year.

Sum borrowed $$= ₹$$20000.

Rate of interest $$=$$ 3$$\%$$ per year.

This means if $$₹100$$ is borrowed, he has to pay $$₹$$3 as interest. So, for the borrowed amount of $$₹$$20000, the interest for one year would be:

$\frac{3}{100}×20000$ $$= ₹$$600.

So, at the end of $$1$$ year, Vijay has to give an amount, which is the sum of principal and interest.

That is $$A = P + I = ₹$$$20000+600$ $$= ₹$$20600.