Sal introduces a very special number in the world of math (and beyond!), the constant e.Created by Sal Khan.
Watch the next lesson:
Missed the previous lesson? Watch here:
Finance and capital markets on Khan Academy: This is an older tutorial (notice the low-res, bad handwriting) about one of the coolest numbers in reality and how it falls out of our innate desire to compound interest continuously.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We’ve also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Finance and Capital Markets channel:
Subscribe to Khan Academy:
source
10:57
'you almost wouldnt mind paying the loanshark E dollars because its such a beautiful number'
What a nice scam.
Sir , u are one of the most amazing math teachers in my life , helping me understand things clearly, in fact Crystal clearly .
Thank u verry much.
This is the beauty of mathematics
'You almost wouldn't mind paying the interest of this mystical number'
Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it. '
(ALBERT EINSTEIN)
hahah Sal was in a good mood and agreed to lend you money for a "low interest": 100% a year. So funny when you think it as how you were fooled by some loan guy.
I got excited learning about this. Which really makes sal he BEST teacher I could have.
Yeah, but after x periods, you owe (1+1/n)^(n*x), and that's no good. The rate is 1/n, which becomes increasingly appealing for borrowers, but boy does it hurt after compounding. It's basically the question of: "would you rather pay $2 or $e?" Here's a vivid application.
Since the interest per period falls like 1/n, people that are desperate for cash buy things as debt and have to pay back money with interest. These long-period 1/n type loans cause such people to pay back more than they otherwise would. An example of this are 'subprime auto loans', which systematically target low income citizens with bad FICO scores and financial problems. A financially astute individual would never follow a low-interest loan.
Fun fact: in 2015 over $1 trillion was borrowed for US subprime auto loans, for the first time ever (accounting for over 1/3rd of all loan transactions). Yes, ladies and gentlemen, this is how people pay 2, maybe 3 times the value of their asset.
been learning economics independently , and your vids are totally awesome
Anyone else find yourself getting frustrated at the dope who borrows 1 dollar, and then spends 50 dollars worth of the loan shark's time going through hypothetical repayment scenarios? LOL
thnx this helped and i don't even study this because I'm in 6th grade, but it still helped me understand it =)
Masturbate in california…
im studying actuarial science. we use the force of interest quite a lot.
░░░░███████ ]▄▄▄▄▄▄▄▄
▂▄▅█████████▅▄▃▂ ☻/︻╦╤─ BOB ARMY, YOU GOT SURROUNDED
Il███████████████████]. /▌ SURRENDER BEFORE SOMEONE GET HURT
◥⊙▲⊙▲⊙▲⊙▲⊙▲⊙▲⊙◤.. / COPY PASTE THIS TO SURROUND BOB ARMY AND MAKE THEM SURRENDER BEFORE GOOGLE+ CALLS EVEN MORE ARMY, JOIN THE SIGN UP AND CREATE A EVEN BETTER ARMY !
Could you do a video on various limits involving e, not just this one or the factorial one? It would be pretty interesting to see a proof of e = lim x->inf of x/(x!^(1/x))