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.
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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
Pe^rt can be applied to many different scenarios, this is just one of the
possibilities.
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
Pe^rt can be applied to many different scenarios, this is just one of the
possibilities.
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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!
ReplyDeletedennis,
ReplyDeletei like how you gave a brief description of euler's history before you got into your lecture. nice job.
professor little