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Re: Comparing yield between Vanguard MMF and Emigrant Direct?
Old 11-23-2006, 08:17 AM   #21
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Re: Comparing yield between Vanguard MMF and Emigrant Direct?

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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 pre-algebra 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?
Old 11-23-2006, 11:42 AM   #22
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Re: Comparing yield between Vanguard MMF and Emigrant Direct?

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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?
Old 11-23-2006, 01:08 PM   #23
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Re: Comparing yield between Vanguard MMF and Emigrant Direct?

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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?
Old 11-23-2006, 01:55 PM   #24
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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 power-series expansion ?



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Re: Comparing yield between Vanguard MMF and Emigrant Direct?
Old 11-23-2006, 02:09 PM   #25
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Re: Comparing yield between Vanguard MMF and Emigrant Direct?

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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 power-series 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?
Old 11-23-2006, 02:32 PM   #26
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Re: Comparing yield between Vanguard MMF and Emigrant Direct?

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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?
Old 11-24-2006, 09:51 AM   #27
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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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