Compound Interest

Compound Interest Formula 

Compound interest: At the end of the interest cycle, if the interest is getting added to the sum, initially borrowed, to create a new principal, then this kind of arrangement is called as compound interest.

 In compound interest for the new cycle , interest is calculated on the sum borrowed plus on the accumulated interest.

 Formula for calculating compound interest

Amount = P { 1 +  (r/100)}t               Where,                                                                       P = Principal Amount or the amount that was initially lend                                    r = rate of interest per annum at the principal was borrowed                                    t = time period ( in years ) for which the amount was borrowed

Some Important Formulas:

1. If interest is compounded Quarterly

    If the interest is compounded quarterly, 
    then,
    the time 't' in years becomes (t/3) as there are 4 quarters in a year of 3 month each
    and the rate of interest r becomes (r/3).
    And the formula for compound interest becomes

                    Amount = P [ 1 +  {(r/3)/100}]^t/3   

2. If interest is compounded Monthly
    If the interest is compounded monthly, 
    then,
    the time 't' in years becomes (t/12) as there are 12 months in a year
    and the rate of interest r becomes (r/12).
    And the formula for compound interest becomes

                    Amount = P [ 1 +  {(r/12)/100}]^t/12  

      


Q1. The compound Interest on Rs. 1,800 at 10% per annum for a certain period of time is 378. Find the time in years
(a)  3 years     (b) 2.5 years
(c)  2 years   (d)  2.8 years

Answer:(c)  2 years
Solution:
Using the formula used above, we have

         2178 = 1800(1 + 10/100)^t 
 =>    1.21 = (1.1)^t


            => t = 2       Because 1.1²= 1.21

Q2. The difference between the simple and compound interest on a certain sum of money for 2 years at 4% per annum is Rs.1. Find the sum.
(a) Rs .630           (b) Rs. 620
(c) Rs. 625          (d) Rs. 635

Answer:(c) Rs. 625  
Solution:
Let the number be X then 
Simple Interest at the end of 2nd year  = (X x 4 x 2)/100 = ( X x 8)/100 = (2X)/25
Compound Interest at the end 2nd year = A - P = X {(1 + 4/100)2 - 1  }=  X(0.0816)

Again it is given that the difference between the two types of interest is Re 1
Therefore,
                    0.0.0816X - (2X)/25 = 1
             =>   X(0.0816 -0.08 )     =1
             =>   X(0.0016)  =1
             =>  X = 1/0..0016 = 625