6 ms·
Bernoulli discovered e by studying a question about compound interest
- jiggy2011 14y agoSo, XKCD. http://xkcd.com/947/ http://xkcd.com/947/
- gabriel34 14y agoWell, he is investing at about 0.15% per month =)
- eliben 14y agoCalculus 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 14y agoYeah, but someone actually had to discover that at some point in the past ;)
- alecst 14y 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 14y agoIt 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%A6 http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%80%...
- alecst 14y agoMy mistake, didn't notice the minus sign...
- RockofStrength 14y agoHere's my "e bookshelf" http://imgur.com/YBB33 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 14y agoAnother 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 14y agoIn 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 14y agoFunny 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 14y agoIt 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_versus_effective_interest_rate http://en.wikipedia.org/wiki/Nominal_interest_rate#Nominal_v...
- tcgv 14y agoThis 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%20Early%20Transcendentals/upfiles/projects/ecet_wp_0307_stu.pdf http://www.stewartcalculus.com/data/ESSENTIAL%20CALCULUS%20E...
- samatman 14y agoThere is more than one famous Bernoulli. This is the work of Jacob Bernoulli; Daniel Bernoulli, of Bernoulli's principle, is arguably better known.
- sonabinu 14y agoThere is a great book out there called ' Against the Gods ' by Peter Bernstein. http://www.amazon.com/Against-Gods-Remarkable-Story-Risk/dp/0471295639 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 14y agoWhat can't compound interest teach us....