

Bernoulli discovered e by studying a question about compound interest - sthlm
http://en.wikipedia.org/wiki/E_(mathematical_constant)#Compound_interest

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samatman
There is more than one famous Bernoulli. This is the work of Jacob Bernoulli;
Daniel Bernoulli, of Bernoulli's principle, is arguably better known.

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raverbashing
Funny how the calculation seems to be done backwards

(For an initial 100% interest) "If the interest is credited twice in the year,
the interest rate for each 6 months will be 50%"

And of course this is wrong, because the interest is not 50% but (2^1/2) - 1
(that is, 41%) since x * 1.4142(first interest payment) * 1.4142(second
interest payment) should be 2*x

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rjtavares
It isn't wrong, it's just a convention in finance. The Nominal Annual Rate is
presented "without adjustment for the full effect of compounding" [1]. In the
provided example, a 100% nominal annual rate becomes a 125% effective annual
rate, since it is credited twice in the year.

[1]
[http://en.wikipedia.org/wiki/Nominal_interest_rate#Nominal_v...](http://en.wikipedia.org/wiki/Nominal_interest_rate#Nominal_versus_effective_interest_rate)

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sonabinu
There is a great book out there called ' Against the Gods ' by Peter
Bernstein. [http://www.amazon.com/Against-Gods-Remarkable-Story-
Risk/dp/...](http://www.amazon.com/Against-Gods-Remarkable-Story-
Risk/dp/0471295639) It has the fantastic story of how a lot of mathematical
computations are a product of the effort to quantify risk.

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tcgv
This reminds me of something a professor told me in my first Calculus course
that the famous L'Hospital's rule, named after the French mathematician
Guillaume de l'Hôpital, was actually discovered and proved by Bernoulli. The
saying is that l'Hospital bought the rights to Bernoulli's mathematical
discovery in order to publish it in his book _Analyse des Infiniment Petits
pour l'Intelligence des Lignes Courbes_ [1]

[1]
[http://www.stewartcalculus.com/data/ESSENTIAL%20CALCULUS%20E...](http://www.stewartcalculus.com/data/ESSENTIAL%20CALCULUS%20Early%20Transcendentals/upfiles/projects/ecet_wp_0307_stu.pdf)

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jiggy2011
So, XKCD. <http://xkcd.com/947/>

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gabriel34
Well, he is investing at about 0.15% per month =)

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RockofStrength
Here's my "e bookshelf" <http://imgur.com/YBB33> , which uses the 1/n!
definition. It only goes up to 1/3!, but ideally would approach 1/infinity!. e
grows as the total area of the clear books on the left. For example, for the
bottom shelf, 1/3! is the same as having all possible arrangements of three
objects, and choosing one.

~~~
defen
Another nice property of the 1/n! definition is that you can use it to define
exponentiation for things which don't have division (e.g. matrices)

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eliben
Calculus 101?

I recall that learning that lim(1 - 1/n)^n with n->inf is 1/e, was one of the
first things learned in Calculus. I think we even briefly touched this in
highschool.

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alecst
> I recall that learning that lim(1 - 1/n)^n with n->inf is 1/e

To clarify this should not be 1/e, but e.

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evanb
It would be e if there had been a + sign in the parens, but with a - it is, in
fact, 1/e. (1-1/n) is always less than 1; multiplying a bunch of factors less
than 1 can't possibly* give you 2.something.

*without somehow wrapping around infinity [http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%80%...](http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%80%A6)

~~~
alecst
My mistake, didn't notice the minus sign...

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lurkinggrue
What can't compound interest teach us....

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vegas
In other breaking news of interest to the digitally connected elite, e follows
d and precedes f. It is also generally not used as a grade in American
educational institutions.

