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Short Trick Method For Compound Interest Problems



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


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 Years B. 3 Years C. 4 Years D. 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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