Talk:2768: Definition of e
This is of course one way of arriving at the value of e: https://en.wikipedia.org/wiki/E_(mathematical_constant)#Compound_interest Trimeta (talk) 03:55, 27 April 2023 (UTC)
One explanation may be that Miss Lenhart is in a Ponzi scheme. Ponzi schemes claim to offer unbelievably high returns that are actually paid by later investors, it will invariably crash, but by the time, the scammers will have vanished with the money. Here, Miss Lenhart effectively offers +172% annual returns, which is way above what a honest bank can offer, and she seems to push the student into investing, which is aligned with the Ponzi scheme goal of getting as many people to invest as possible. 220.127.116.11 11:25, 27 April 2023 (UTC)
e^iπ + 1
- i is not a number, it is the imaginary unit. SDSpivey (talk) 16:00, 27 April 2023 (UTC)
- i is a number. 1 is also sometimes called the unit by mathematicians. 18.104.22.168 21:01, 27 April 2023 (UTC)
- Every number is an inherent feature of mathematics, but I don't think the number e is as special as formulas like this make it appear. What's really significant is the exponential function exp, and the number e is just exp 1. It is therefore similar in significance to √2 or ln 2. Similarly, in the identity you provide, the general form is exp iθ = cos θ + i sin θ, and plugging in θ = π is just one special case. EebstertheGreat (talk) 02:33, 28 April 2023 (UTC)
- e^ipi is genuinely quite boring. I would prefer e^i2pi = e^0 = 1 because its more immediately apparent that e^ix forms a circle/periodic function22.214.171.124 06:29, 28 April 2023 (UTC)
Does anyone else see the buttons at the top as being weird? The first comic arrow is split into two buttons separated by a new line. 126.96.36.199 12:24, 27 April 2023 (UTC)
Maybe the bank was originally owned by Beret Guy? That would explain why it continues to stay in business despite effectively giving away money. It's not suggested anywhere in the comic, but the idea is very much in line with his powers. 188.8.131.52 13:40, 27 April 2023 (UTC)
The current explanation is vague regarding the identity of the speaker in the title text, but it seems clear to me that the title text is being said by Miss Lenhart - she's explaining how she came into possession of the bank account in question. Her high school teacher set it up, and then she engineered the takeover so she could continue to use the account after passing the class. Snuffysam (talk) 16:12, 27 April 2023 (UTC)
r = n * (2^(1/n) - 1)
This demonstrates a misunderstanding of the way banks, and other financial institutions, quote interest rates. A bank that pays 100% interest rate annually, will pay $1 on 1$: at the end of the first year the balance will be $2.00. That is not (1+100%/n)**n, and is not $2.71, because the interval compounding rate is not 100%/n for n <>1. The interval compounding rate for 100% per annum is r = n * (2^(1/n) - 1). I leave working out the limit as n approaches infinity as an exercise for the reader :) I don't know if math teachers in the USA actually use this example as a math teaching method: if so, they should certainly have a discussion with a 'business studies teacher' or 'business math teacher' about the meaning of the words they are using, because they are doing a disservice to students by misleading them about the meaning of common savings and loan terms of business.
- This would mean there is no difference between interest “compounded annually” vs. “compounded daily”? Also, deleted the last paragraph of the exp. Seems clear to me that the title text speaker is the student in the strip, later relating the very incident illustrated. (And no need for comment on characters’ future business endeavors.) Miamiclay (talk) 10:58, 4 May 2023 (UTC)
- Unremoved the last para. The teacher deecribed is male, Miss L is not. But if the suggestion is that the narrating person is Miss L (after the year has passed?), then we have other problems to explain (how she thinks she got it to work, hypercompetent as she is but as impossible the setup is).
- I read it as someone else, off-panel (traditionall Randall's voice, but not in this case?), who is describing a different time and who clearly didn't/doesn't grasp reality (did not get taught/listen that well, at school, seems convinced they did something clever), or can actually ignore the problems (like Beret Guy). But it could do with streamlining. Or various brief arguments for and against who is saying it, split up. 184.108.40.206 12:35, 4 May 2023 (UTC)
- I initially (mis?)read “his bank” as reflecting not ownership, but where he banked, but you’re probably right. Either way, the whole thing seems both unclear as to the referents and somewhat misconceived - When a bank pays absurdly high rates, the last thing one would want is to acquire it! Miamiclay (talk) 15:09, 4 May 2023 (UTC)
- The difference between "compounded annually" and "compounded monthly" was/is that "compounded monthly" is computed on the "minimum monthly balance". Savings banks moved to "compounded daily" when computers meant that the work involved wasn't completely unreasonable. With "compounded daily", you get paid interest even if you have one day in the month when the balance was $0.01 and all the other days were $100K.
- If you are buying a 90 day bond, the interest really is quoted as n*90/365 (or n*90/360, or n*90/366 or %90/90, depending on the exchange rules). And if you re-invest, you get more. And you can do the same with over-night money (daily rollover). But that's "re-investment", not "daily-compounding". And the thing is, working out "true cost" is difficult for most people, and most people don't know and haven't thought about what "daily compounding" is, and probably wouldn't understand the math if they do think about it. It's easy to believe that teachers are miss-using the business terms used for ordinary savings accounts, but if so, that's unfortunate.
As it stands, this explanation smacks of taking the fictional scenario way too literally. It spends a lot of words deconstructing the idea of "100% annual interest", instead of explaining the comic. My interpretation is that we're meant to take the 100% at face value: it shouldn't work, but it does. -- Peregrine (talk) 01:41, 6 May 2023 (UTC)
It's just the difference between measuring interest in APY and APR. A 100% rate compounded every minute has a 172% yield. The teacher must be talking about rate, because that's the only way to get $e at the end. EebstertheGreat (talk) 03:32, 14 May 2023 (UTC)