The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

A New Interpretation of the Number e


Olivier de La Grandville

Faculty of Economics, Goethe University,
Frankfurt, Theodor-Adorno Platz 4,
60323 Frankfurt am Main,


We show that e is the amount that 1 becomes when it is invested during an arbitrary time span of length T, at any continuously compounded interest rates as long as their average is equal to 1/T . A purely mathematical interpretation of e is the amount a unit quantity becomes after any duration T when the average of its instantaneous growth rates is 1/T. This property can be shown to remain valid if T tends to infinity as long as the integral of the growth rates converges to unity.

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