Bernoulli discovered e by studying a question about compound interest
1–10 of 17 posts
Re: Bernoulli discovered e by studying a question about compound interest
#2So, XKCD.
http://xkcd.com/947/
Re: Bernoulli discovered e by studying a question about compound interest
#3Calculus 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.
Re: Bernoulli discovered e by studying a question about compound interest
#4Here'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.
Re: Bernoulli discovered e by studying a question about compound interest
#5So, XKCD. http://xkcd.com/947/
Well, he is investing at about 0.15% per month =)
Re: Bernoulli discovered e by studying a question about compound interest
#6Calculus 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.
Yeah, but someone actually had to discover that at some point in the past ;)
Re: Bernoulli discovered e by studying a question about compound interest
#7In 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.
Re: Bernoulli discovered e by studying a question about compound interest
#8Funny 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
Re: Bernoulli discovered e by studying a question about compound interest
#9Funny 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
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...
Re: Bernoulli discovered e by studying a question about compound interest
#10This 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...