Bernoulli discovered e by studying a question about compound interest

http://en.wikipedia.org/wiki/E_(mathematical_constant)#Compound_interest

by sthlm • 14 years ago

51 16 14 years ago

en.wikipedia.org

jiggy2011• 14 years ago

So, XKCD. http://xkcd.com/947/

gabriel34• 14 years ago

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

eliben• 14 years ago

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.

maaku• 14 years ago

Yeah, but someone actually had to discover that at some point in the past ;)

alecst2• 14 years ago

> 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.

evanb• 14 years ago

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%...

RockofStrength• 14 years ago

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• 14 years ago

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)

vegas• 14 years ago

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.

raverbashing• 14 years ago

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

rjtavares• 14 years ago

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...

tcgv• 14 years ago

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...

samatman• 14 years ago

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

sonabinu• 14 years ago

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

lurkinggrue• 14 years ago

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

Bernoulli discovered e by studying a question about compound interest

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