**is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan.**

*Compound interest*###
*Normal Method :*

*Normal Method :*

Amount = P ( 1 + r/100)^t

Here P = Principle

r = Rate

t = Time period

**Example :**

*Find the compound interest on Rs. 7500 at 10% per annum for 2 years, compounded annually.***Solution :**

Amount = 7500(1 + 10/100)2 = 9075

Interest = Amount - Principle = 1575

###
**Tricky Method :**

Compound Interest Formulas

For 2 Years = 2 ( ) + 1( )

For 3 Years = 3( ) + 3 ( ) + 1( )

For 4 Years = 4( ) + 6 ( ) + 4 ( ) + 1 ( )

**Example:**

Find the compound interest on Rs. 7500 at 10% per annum for 2 years, compounded annually?

**Solution :**

Compound Interest = 2( A ) + 1 ( B )

= 2 ( 10% of 7500) + ( )

= 2(750) + 1( )

A = 10% of 7500 750

B = 10% of A = 10% of 750 = 75

= 2(750) + 1 (75)

= 1575

**Note :**By using normal method its difficult when powers increasing and rate is not in 10 or 5 multiples.

### Example :

## Ques 1.

What will be the compound interest on Rs. 25000 after 3 years at the rate of 12 % per annum ?

**Solution :**

Compound Interest = 3 ( A)+ 3(B ) + 1 ( C)

A = 12% of 25000 = 3000

B = 12% of A = 12% of 3000 = 360

C = 12% of B = 12% of 360 = 43.2

= 3 ( 3000) + 3 ( 360)+ 1( 43.2 )

= 9000 + 1080 + 43.2

= 10,123.2

## Ques 2.

What will be the compound interest on Rs. 25000 after 4 years at the rate of 10% per annum ?

**Solution :**

Compound Interest for 4 years

= 4 (A)+ 6(B) + 4(C)+1(D)

A = 10% of 25000=2500

B = 10% of 2500 = 250

C = 10% of 250 = 25

D = 10% of 25 = 2.5

= 4(2500)+6(250)+4(25)+1(2.5)

=10000 + 1500 +100+2.5

=11602.5

## Ques 3.

At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?

A. 3%B. 4%C. 5%D. 6%

**Solution :**

Assume rate = x

Compound Interest = 1348.2 - 1200= 148.2

==> R % of 1200 = 148.32.

==> R = 148.32/12 = 12.36

here R is for entire 2 years , but we need only one year

==> Rate R = 12.36/2 = 6.18

Now Check Options which rate is near to your rate.

its 6 , so answer is 6%

## Ques 4.

In what time will Rs.1000 become Rs.1331 at 10% per annum compounded annually ?

A. 2 YearsB. 3 YearsC. 4 YearsD. 5 Years

**Solution :**

Compound Interest = 1331-1000 =331

100% ----- 1000

X% ------ 331

==> 331/10 = 33.1(its for 3 years, but we need for 1 year)

Rate = 33.1/10= 3.3 years

Check Options which years is near to your years , Its 3

So Answers is 3 years

**Note :**Our intention is need to select right option in examination , we don't need entire procedure.

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