Euler's Number

... is the base of the natural logarithm and exponential function. Its value is approximately 2.718.

To explain what "the base of the natural logarithm and exponential function" actually means, compound interest is often cited.

If interest is calculated once a year at a rate of 100%, after one year an investment would be worth twice its original value. If interest were calculated twice a year at 50%, the value after one year would be 2.25% of the original investment. As the frequency n increases, and the rate of interest remains at 1/n, the ratio of the final value (after n increases) to the initial value continues to increase; but as n approaches infinity, the ratio tends to Euler's number.

In other words: as n continues to increase, the ratio tends to a little over 2.718.

You now know as much as I do about this topic!

© Haydn Thompson 2025