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What is a compound interest?

Friday 17 February 2023



           The term Interest is the extra money paid by the institutions like banks or 

post offices on money deposited with them. Interest is also paid by the people 

when they burrow money.


      If  we observe the bank statements, we generally notice that some interest is 

credited to our account every year. This interest varies with each year for the same 

principal amount. We can see that interest increases for successive years. Hence, 

we can conclude that the interest charged by the bank is not simple interest; this 

interest is known as compound interest .

What is a compound interest?

       Compound interest is the interest calculated on the principal and the interest 

accumulated over the previous period. It is different from simple interest, where 

interest is not added to the principal while calculating the interest during the next 

period. It is usually denoted by C.I.


What is the formula for finding compound Interest?

 Compound Interest = Interest on principal + Interest over existing interest.
So compound interest formula is given by:

                 compound Interest, C.I = Amount - Principal

            where  Amount ,A is given by:

where  , A = Principal amount

      r = rate of interest

                                                     t = time(no. of the years                                      
                                                      n = no. of times interest is compounded per year                  

             when we substitute A in C.I, we have:

where , C.I = Compound Interest

  r = rate of interest   

         t = time (no. of years)   

                                                 n =  no. of times interest is compounded per year

p = principal         
  Rate Compounded Annually or Half Yearly     

The C.I formula can be expressed for different situations such as the interest rate 

is compounded yearly, half-yearly, quarterly, monthly, daily, etc.     

             if it is compounded annually then then n will be 1 in the given formula
            if it is compounded half yearly for 1 1/2 year then n will be  1+1/2 = 3/2  in the given formula.

 Applications of Compound Interest Formula

There are some situations where we could use the formula for calculation of 

amount in CI. Here are a few. 

(i) Increase (or decrease) in population. 

(ii) The growth of a bacteria if the rate of growth is known. 

(iii) The value of an item, if its price increases or decreases in the intermediate years

Some examples for finding  compound Interest





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