Question
Mon March 05, 2012 By:

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

Expert Reply
Tue March 06, 2012
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. 
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