Why 'E' by Professor Varnell

What is 'E'? Growing up I always saw it on a calculator but never gave it much value. People love talking about pie. No, not pies you can eat like here. I mean 3.14159. In high school, my math teacher would bring it pies for Pie Day! Everyone loved pie day. However, I never really appreciated 'E'. What was it good for?

Before explaining how to find 'e' lets talk about its uses. One cannot appreciate 'e' until one realizes how much money can be made using it. As a kid I used to put money in a piggy bank and hide it under my bed. I thought I was so smart because I was saving up money. What I did not know was that the money I was saving was losing money everyday. Due to inflation one dollar loses value every year. The amount of purchasing power that dollar has is shrinking. What's an example of this?

In 1930 one could get SIX cokes for 25 cents. Crazy. Now Coca-Cola costs almost 1.5 $ at a vending machine. Why? Because money loses value over time.


How can 'e' help reverse that trend? It comes down to interest. Interest is an amazing concept that allows money to grow over time by itself. The modern day financial system is based on letting bank lend out 90% of the money that is deposited in them. Why? Well the bank lends the money out for a certain interest rate and in return gives the person who has deposited the money in the bank( hopefully you or I) a lower interest rate. This interest is what allows our money to grow or at least retain the same purchasing power( also called stagnation) over time.

If one is smart, he or she will try to find the bank that offers the most interest or find the bank that compounds the interest the most. Which is more important? However, there are banks that offer continously compounding interest. Why is this important? If interest is compounded continuously than one can withdraw the money at any point and the amount would have grown. This allows flexibility on withdrawing cash. If interest is compounded quarterly than one should only withdraw money right after it has been compounded.

Now, what is 'e'? The formal equation looks like this:

what happens when we start plugging numbers into the equation for 'n'?
1--->2
2--->2.25
5-->2.48
10-->2.59
100-->2.70
1000-->2.716
10000-->2.718
100000-->2.718

The closer to infinity one solves to the closer to a constant 2.18 the 'e' becomes.

Now to compute continuously compounded interest one uses the formula PERT! Finally a fun sounding formula. It actually looks like 

Now, plug in the amount of money you want to invest, the time, and Bam! You've made money. The concept of 'e' makes more sense to me when I can see it in a real life problem like this one.

I hope you enjoyed the lesson!