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Wednesday, April 23, 2014

The number "e"

Hello Class! 

Today I will explain the importance of the number "e" and it's application to the real world (post grad life) and how you can and will use it in the future.

You may not have heard the name Leonard Euler before, but he is extremely important in this lesson.  It is he whom we owe thanks to for discovering this extremely useful and easily applicable concept.  Euler, a prolific Swiss mathematician and Physicist, was born on April 15th, 1707 and passed away on September 18th, 1783.  This breakthrough concept has made many mathematical concepts possible, like: mathematical notation, analysis, number theory, graph theory, applied mathematics, some physics and astronomy concepts, and many logistic reasoning computations.  I could talk about Euler’s accomplishments forever, but today I will explain to you the number e’s most popular use: the application to exponential growth and money loans.  The number e literally stands for 2.71828.

 

There is a good chance that most of you will have to deal with a loan from a bank at some point in your lives- whether it be in the form of a mortgage, a refinancing, a construction loan, or what have you.  The best way to universally apply growth and the number e to all the possibilities is in the form, Pe^rt.  Pe^rt, or as I remember it as, Pert.   Pert stands for Principal times e raised to the power rate times time.  Lets take a real life scenario and apply it to pert. 

 

20 years from now, you have a family and a pretty solid steady income rolling in.  You decide that you want to start a micro-lending company.  You get your first client, and he wants to borrow $1,000,000 from you because he has terrible credit so he cannot get the loan from the bank.  He plans to start a software company with the loan.  You look over his business plan and it all looks pretty good.  You know that the bank wouldn’t give him a loan at their current 7.2% stated rate so you have leverage over him.  You demand 10% interest with payments made annually over the course of 12 years.  He is hesitant but eventually agrees.  You are excited and want to see how much money you will make off your loan.  The P in the equation is 1,000,000 – the e is just e (or 2.71828) – the r is 10% - and the t is 12.  You set the equation up as 1,000,000e^0.1x12.

 

1,000,000 • e^0.1•12 = $3,320,116.90

 

You are doing pretty well in these tough economic times because you can scoop up all the people who need loans at above average rates because they do not qualify for the bank loans.

Pe^rt can be applied to many different scenarios, this is just one of the possibilities.


Thanks for listening!!!

-DC 

2 comments:

  1. I like how you started with history in your lecture. It was an informative one for me! Leonhard Euler's name is in many field that's related to math somehow. I learned about him after I started using this site that was named after him https://projecteuler.net/. Good job!

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  2. dennis,

    i like how you gave a brief description of euler's history before you got into your lecture. nice job.

    professor little

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