

Re: Comparing yield between Vanguard MMF and Emigrant Direct?
11232006, 07:17 AM

#21

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Location: minnesota
Posts: 13,211

Re: Comparing yield between Vanguard MMF and Emigrant Direct?
Quote:
Originally Posted by justin
I didn't think PEMDAS order of operations was that advanced? It is required to evaluate simple mathematical expressions. 4th grade math from what I recall. Certainly by 6th grade prealgebra it would be taught, right?
Of course, I was one of those guys that finished all of my calculus and diff eq for my engineering degree during high school. 8)

I remember 4th grade. In my school we learned long division and still were working on multiplication table drills. We used to have to stand by our desks and the teacher would give us each a multiplication problem. If you got it wrong you sat down. The last person standing won. Brought out the competitor in me.
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Re: Comparing yield between Vanguard MMF and Emigrant Direct?
11232006, 10:42 AM

#22

Full time employment: Posting here.
Join Date: Jul 2005
Posts: 987

Re: Comparing yield between Vanguard MMF and Emigrant Direct?
Quote:
Originally Posted by HFWR
Well, you do have to enter it into a calculator this way...

don't need any parens on my calculator (no parens, no equal key)
.508 enter 365 / 1 + 365 ^ 1 
done
love RPN!
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Re: Comparing yield between Vanguard MMF and Emigrant Direct?
11232006, 12:08 PM

#23

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Join Date: Dec 2002
Location: Oahu
Posts: 26,563

Re: Comparing yield between Vanguard MMF and Emigrant Direct?
Quote:
Originally Posted by FIRE'd@51
Let A = (1 + R/N)^N = value of $1 in a year
Ln A = N Ln (1 + R/N) where Ln is the natural log
as N goes to infinity, Ln (1 + R/N) ~ R/N
Ln A ~ N x (R/N) = R
therefore A = e^R
if R = 0.05 , A = e^0.05 = 1.05127 so the continuously compounded APR = 5.127%

"This is your brain on bond funds. Any questions?"
Quote:
Originally Posted by bosco
love RPN!

I was wondering when that would come up. It's the mathematics equivalent of Godwin's law...
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Re: Comparing yield between Vanguard MMF and Emigrant Direct?
11232006, 12:55 PM

#24

Full time employment: Posting here.
Join Date: Sep 2006
Posts: 608

Re: Comparing yield between Vanguard MMF and Emigrant Direct?
Quote:
Originally Posted by FIRE'd@51
Let A = (1 + R/N)^N = value of $1 in a year
Ln A = N Ln (1 + R/N) where Ln is the natural log
as N goes to infinity, Ln (1 + R/N) ~ R/N
Ln A ~ N x (R/N) = R
therefore A = e^R
if R = 0.05 , A = e^0.05 = 1.05127 so the continuously compounded APR = 5.127%

Wow, cool. The good old natural logarithm.
But I don't quite see why it's obvious that Ln(1+R/N) goes to R/N
as N goes to infinity (even though a calculator quickly reveals that it's true).
Perhaps the powerseries expansion ?
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Re: Comparing yield between Vanguard MMF and Emigrant Direct?
11232006, 01:09 PM

#25

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Join Date: Aug 2006
Posts: 2,241

Re: Comparing yield between Vanguard MMF and Emigrant Direct?
Quote:
Originally Posted by JohnEyles
But I don't quite see why it's obvious that Ln(1+R/N) goes to R/N
as N goes to infinity (even though a calculator quickly reveals that it's true).
Perhaps the powerseries expansion ?

Yep, for 1 < x < 1, Taylor expansion for Ln (1 + x) = x  (1/2) x^2 + (1/3) x^3  ...............
If x << 1, then Ln (1 + x) ~ x , since other terms in alternating series go to 0 much faster
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Re: Comparing yield between Vanguard MMF and Emigrant Direct?
11232006, 01:32 PM

#26

Thinks s/he gets paid by the post
Join Date: Oct 2006
Location: NorthCentral Illinois
Posts: 3,181

Re: Comparing yield between Vanguard MMF and Emigrant Direct?
Quote:
Originally Posted by setab
This whole string reminds me of why I put my funds somewhere and forget them. I can do the equations, but don't want to.
setab

Geesh!!! Ya got that right!!! :P
I'm soon to be FIRE'd as a laboratory manager, and look forward to a MAJOR lack of equations in my daily life!!!
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Re: Comparing yield between Vanguard MMF and Emigrant Direct?
11242006, 08:51 AM

#27

Full time employment: Posting here.
Join Date: Jul 2005
Posts: 987

Re: Comparing yield between Vanguard MMF and Emigrant Direct?
Quote:
Originally Posted by Nords
"This is your brain on bond funds. Any questions?"
I was wondering when that would come up. It's the mathematics equivalent of Godwin's law...

Hitler liked RPN too!
(=Godwin ^ 2)
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