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Alternative Proof of this Time Value of Money Theorem

764dak · 2015-06-24 05:03:26

Let t = time, i = interest Simple interest is s = 1+ti Compound interest is c = (1+i)^t Prove that For 0<t<1, (1+i)^t < 1+ti Proof: Define a function g:[0,infinity) ->R by g(i) = c-s = (1+i)^t - (1+ti) For g(0) = 0 and g'(0) <0 for 0<t<1 and i>0. This proves it but I want an alternative proof that doesn't use calculus. Can…

24-06-2015 5:03am

#1

764dak

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Let t = time, i = interest
Simple interest is s = 1+ti
Compound interest is c = (1+i)^t

Prove that
For 0<t<1, (1+i)^t < 1+ti

Proof:
Define a function g:[0,infinity) ->R by g(i) = c-s = (1+i)^t - (1+ti)
For g(0) = 0 and g'(0) <0 for 0<t<1 and i>0.
This proves it but I want an alternative proof that doesn't use calculus. Can any of you provide one?

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#2 26-06-2015 4:02am

A Primal Nut

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(1+i)^t < 1+ti
t+ti < 1 + ti
t<1

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