**Basics of Simple Interest & Compound Interest (SI and CI Basic concept)**

**INTEREST DEFINITION: **

It is the money paid for the use of money borrowed. it is paid quarterly, half yearly or annually as agreed upon.

**PRINCIPLE ****DEFINITION****:**

The actual money borrowed is called principle.

**AMOUNT DEFINITION:**

The sum of principle and interest money is called as amount.

**TIME DEFINITION:**

Time is the period at which money is borrowed, n is expressed in number of periods which is normally 1 year.

**SIMPLE INTEREST:**

If throughout the loan period, interest is charge on the original sums borrowed, it is called simple interest.

**SIMPLE INTREST FORMULA:**

Principle,

**1. P= S.I*100/r*n**

2. Simple interest,

**S.I =P*n*r/100**

3. Time

**n= S.I*100/P*r**

4. Rate

**r= S.I.*100/P*n**

**Amount(A)= Principle+ Simple interest**

**EXAMPLE;**

QUE.

Rohit borrowed Rs. 50000 from Roshan at simple interest. After 3 years, Roshan got Rs. 3000 more than what he had given to Rohit. what was the rate of interest per annum?

Ans.

Principle Amount= 50000

Time=3 year

Simple interest= 3000

we know that,

S.I =P*n*r/100

then,

r= S.I*100/P*n

r=3000*100/5000*3

r=2%

**COMPOUND INTEREST:**

Money is said to be lent at compound interest when the interest due after a given time is added to the principle goes on increasing at the end of every year by an amount to the interest for that year. Difference between final amount and the original principal is called compound interest.

**Compound interest FORMULA (C)**

**C= P[(1+r/100)^n-1]**

C= Compound Interest

P= Principal(original balance)

r= rate per period

n= number of periods

**REMEMBER:**

- Compound interest for 1 year is equal to the simple interest for one year.
- The difference between C.I and S.I on the same sum for 2 years is one year interest on the S.I for 1 year.

**EXAMPLE:**

Que. Rs. 2000 is invested for 2 year at 5% compound interest per year. what is the total interest earned over the four years?

Ans:

Principle amount= 2000

Time= 2 year

Interest Rate=5%

we know that, compound interest= P[(1+r/100)^n-1]

Put these all values in equation

C=2000 [(1+5/100)^2-1]

C=205 rs

**COMPARISON OF SIMPLE INTEREST AND COMPOUND INTEREST**

In case of simple interest the principle remains the same for any fixed time period whether for 1st year 2nd year or 3rd year . while in case of compound interest, the principle keeps on increasing as the amount after 1st year become the principle for the second year , amount after two years becomes the principle for the third year and so on.

*The table below shows how an initial investment of 1000 rs can grow in 5 years, if the interest rate is 6%:*

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