What is the significance of the number e (Euler's number)?

The irrational number e is one of the most important numbers in mathematics. The value of it is 2.718... but since it is irrational that is e to 4 significant figure, only. How can we calculate this number? There are many ways to do this and one of the simplest methods is to think about interest rates on savings accounts. We start with a £1 saving and Bank of Sol will give you 100% interest per annum; after 2 years you end up with double your money! But now I offer you a new deal: 50% interest TWICE per annum. Is this a better deal? Yes. Let us see why: After 6 months I have £11.5 = £1.5 and after another 6 months I have £1.51.5 = £2.25. We ended up with more money! So what happens if we keep doing that? We end up with an expression somewhat like this,£1 * (1+ 1/n )^n ~ e as we take the limit of n to ∞ This is one way of working out Euler's number. Euler himself however used a much more complicated method of working out this number. ({n=0}{∞}∑1/n). Applications of e include natural exponential growth, compound interest, and interesting properties regarding its area and gradient when plotted as a graph. (Plot the graph of e^x and also the limit graph, write the equation out and sketch the gradient and area integral)