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Compound Interest and e (part 2)


Compounding 100% annual interest continuously over a year converges to e (2.71...)

Channel: Education
Uploaded: November 30, 1999 at 12:00 am
Author: khanacademy

Length: 10:14
Rating: 4.8974357
Views: 11277

Tags: Continuously  Compounding  interest  finance  math  limit  

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qatari5898700 (November 30, 1999 at 12:00 am)
Khan, you are amazing !!I understand from you more than professor and books !!I hope that the world could appreciate you in your great videos which helped thousands of people in this world.Im sure in near future you will be a difficult number in the education field.
rinwhr (November 30, 1999 at 12:00 am)
@Fanglez yeah
Fanglez (November 30, 1999 at 12:00 am)
is the 'squeeze theorem' learnt in university?
mochilla777 (November 30, 1999 at 12:00 am)
garymarkhov, what's ya problem man ? :) the limit theorem on e is one of the basic facts of algebra. the number you're referring to is acutally 2.71812669161791 ( and it's not like waaaay morethan 2.71443) keep it real yourself :)
garymarkhov (November 30, 1999 at 12:00 am)
Sal, your videos are teh awesome! Thanks so much.Minor note: (1+1/8760)^8760 is waaaaaaaaaaaay more than 2.714433. I know that's what you get if you just use 0.000114, but when you're raising that beasty to the power of 8760, the stuff that comes after the billionths place MATTERS! The correct number is 2.71812666444. Come on man, didn't you notice something was up when the hourly compounded figure came out lower than the daily compounded figure?Keep it real :)
andyct1982 (November 30, 1999 at 12:00 am)
okay
OntologicalQuandary (November 30, 1999 at 12:00 am)
correct, but 1 exists. The squeeze theorem says if two limits approach 1 (or some number that EXISTS) and there is an unknown limit that is between those two limits, it HAS to be the same limit. You can't squeeze to infinity, because one of the equations would have to be "less than infinity" and the other would have to be "more than infinity" which are both nonsense descriptions because infinity doesn't exist in the same sense than 1 does.
andyct1982 (November 30, 1999 at 12:00 am)
i think there are an infinite amount of numbers between numbers. like 0.99999--> infinite 9's til i get to 1. something like that. but never approach 1.
andyct1982 (November 30, 1999 at 12:00 am)
i think there is an infinite amount of numbers that approach that point. like 0.99999---> infinite 9's til i get to 1.0, or something like that.
OntologicalQuandary (November 30, 1999 at 12:00 am)
lol what? I am just saying you cant squeeze something as it approaches infinity. You need a definite point to squeeze prove a limit