please mathematically prove that interest of given period of time is sum of all interest compounded during that period.

Asked by  | 5th Mar, 2012, 04:02: PM

Expert Answer:

Let for the first year onthe principal amount P , rate r% , I be the interest
So , I = P*r*1/100 = pr/100 , Amount = p + I = p(1+r/100)
 
For the second year P = p(1+r/100) , r = r%
So , Again interest I = p(1+r/100)r/100 , Amount = pr/100 + I = p(1+r/100)(1+r/100) = p(1+r/100)^2
As we go on more n number of years we get
Amount = p(1+r/100)^n which is sum of the principal amount and all interest compounded during that period. 

Answered by  | 6th Mar, 2012, 07:01: AM

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