Attacking Problems in Logarithms and Exponential Functions by David S. Kahn

Author:David S. Kahn [David S. Kahn]
Language: eng
Format: epub
Publisher: INscribe Digital
Published: 2015-07-20T16:00:00+00:00

Suppose we went to a bank that offered to pay us interest continuously? Then N would become infinite and our formula wouldn’t work. This was a question that puzzled mathematicians for a long time and was finally answered by Leonhard Euler. He found that if we write the term and we let N become infinity (this is called “finding the limit”), then we get a constant, which was named e, in his honor. We will find that e is a very important number and shows up in all sorts of mathematical contexts, just as π does. The value of e is approximately 2.71828. As with π, it is irrational, so we generally work with an approximation, or we write answers in terms of e. So, if the interest is compounded continuously, our formula changes:

If we deposit P dollars in the bank, at a rate of R % annually, for T years, compounded continuously, we end up with an amount F, where F = PeRT.

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