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.
