In this section, the following topics are discussed with examples

**Basic Entities****Simple & Compound Interest****Rate of interest calculation****Examples**

### Basic Entities

P = Principle = Any sum of money that is either borrowed or received.

**R%= Rate of Interest** = some percentage is levied on that sum of money that is either borrowed or received always calculated on per annum basis.

**n = No of years** = The above said percentage is levied for a particular term of years.

**I = Interest** = for a certain number of years & for a certain rate of interest we will be gaining some amount and that amount is interest

**A= Amount** = P + I = the total outcome of principle with interest

### Simple Interest

In simple interest, the rate of interest on the sum that is invested in the first year is calculated as such that for every year the interest will be same.

S.I. = (PNR/100)

### Compound Interest

In compound interest, the interest will be added back to the sum after each and every year and the rate of interest is calculated for each years added sum and interest.

C.I. = P [ 1+ ( r / 100 ) ]^{n} – P (for interest alone)

C.I. = P [ 1 + ( r / 100 ) ]^{n} ( for amount after n years )

### RATE OF INTEREST CALCULATION

Rate of interest is always being calculated under per annum basis. So we must read the question carefully because in few question they may ask that interest being calculated under these two situations

### i) Calculated Per Half Annum :

A half year is six months and we have two six months in a year so when the question is being asked for half yearly we have to divide rate of interest into half but multiple no of years tol its twice

n = n ( p.a. ) * 2

r = r ( p.a. ) / 2

### ii ) Calculated per quarter annum:

Similarly a year has four quarters in it so this will be for quarterly computed problems

n = n ( p.a. ) * 4

r = r ( p.a. ) / 4

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#### Example 1

A sum of Rs. 25000 becomes Rs. 27250 at the end of 3 years when calculated at simple interest. Find the rate of interest.

**Sol:**

Principle = 25000, so interest would be ,

Simple interest = 27250 – 25000 = 2250

Number of years = 3 years.

SI = PNR / 100

R = SI * 100 / PN

R = 2250 * 100 / 25000 * 3

.`. R = 3%.