We know that , Compound Interest = Amount - Principal money
So, Compound Interest =  p 1   +   r 100 t   -   p
Q: Derive the formula for Amount i.e  p 1   +   r 100 t in Compound interest without taking any certain examples.
{{Derive this by using concepts that can be universally applicable as a derivative.}}


Dear Student,
Compound Interest in nothing but Simple interest for first year then for next year amount becomes the PrincipalSo, using the basic definition let's derive formula for compound interestAssumingPrincipal be pRate of Interest be r% per annumtime be t yearsSo, for 1 yearSI1=p×r×1100Amount=p+SI1(Amount)1=p+pr100 {(Amount)1 means Amount at the end of first year}(Amount)1=p(1+r100).........................................1Now (Amount)1 becomes the principal for next yearSo, for 2nd years (time=1year) SI2=(Amount)1×r×1100(Amount)2=(Amount)1+SI2(Amount)2=(Amount)1+(Amount)1×r×1100(Amount)2=(Amount)1{1+r100}(Amount)2=p(1+r100){1+r100}(Amount)2=p(1+r100)2Similarly,Amount after 't' years will be(Amount)t=p(1+r100)t
Hope this information will clear your doubts about topic.

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