Comparing yield between Vanguard MMF and Emigrant Direct?

[soupcxan]

A simple question, but which is the better place for my spare cash?

1) Vanguard's Prime MMF advertises a yield of 5.08% which is "7 day average income yield net of expenses". However, this rate fluctuates throughout the month, and I'm not sure if I need to annualize this rate to reflect compounding (daily? weekly? monthly?).

2) Emigrant Direct offers an interest rate of 4.93% which is a 5.05% APY, it looks like that's daily compounding.

 

[REWahoo]

Unless your "spare cash" is 100k or more, there isn't enough difference to worry about. I'd go with whichever is more convenient.

 

[Patrick]

Eloan @ 5.5%. www.eloan.com

 

[d]

to compare rate you need to convert the VMMP 7-day yield to an APY.
=(1+5.08/365)^365 -1= 5.21%

 

[bosco]

to compare rate you need to convert the VMMP 7-day yield to an APY.
=(1+5.08/365)^365 -1= 5.21%

lest you try this at home and get 154% yield, the correct formula is

=(1+.0508/365)^365-1 = 5.21%

 

[d]

lest you try this at home

woops!

 

[HFWR]

Not to nitpick, but shouldn't it be:

=((1+.0508/365)^365)-1 = 5.21%

 

[justin]

Not to nitpick, but shouldn't it be:

=((1+.0508/365)^365)-1 = 5.21%

Not to nitpick ( ), but your added set of parenthesis are not needed if you follow the standard order of operations (parenthesis, exponents, multiplication, division, addition, then subtraction).

 

[retire@40]

Not to nitpick ( ), but your added set of parenthesis are not needed if you follow the standard order of operations (parenthesis, exponents, multiplication, division, addition, then subtraction).

That reminds me of the one thing I remember from 8th grade math:

Please
Excuse
My
Dear
Aunt
Sally

 

[justin]

PEMDAS - best thing learned in 4th grade fer sure.

 

[retire@40]

PEMDAS - best thing learned in 4th grade fer sure.

You learned that in 4th grade? You must have gone to school with JG in the advanced section.

 

[JohnEyles]

Not to nitpick, but shouldn't it be:

=((1+.0508/365)^365)-1 = 5.21%

Not to nitpick, but this formula is accurate only for DAILY compounding.
I'm not sure if this is how it's done, or not. Doesn't really matter though.

If you generalize the formula as (1+APR/N)^N - 1, where N is the number
of compounding periods in a year, you'll find that for N=12 (monthly
compounding) 5% -> 5.116%, and for N=365 (daily compounding)
5% -> 5.127%. In fact, you can imagine the limit, as N goes to infinity,
of this expression; I'm a little rusty on how to compute the limit, but
you could approximate it with N=1,000,000, and it's still 5.127%
(you have to go out more decimal places to see the difference).

Even rolling 3-month T'Bills gives you 5.095%; in other words, N=4
gets you 3/4'ths of the way from APR to inifinitely compounded APY
(hope I'm using APR and APY correctly, but you know what I mean).

 

[lazyday]

ED has FDIC insurance, which should be worth something. There's a 1% chance per year, of a hundred year flood.

(I'm thinking of a financial "flood" that hurts money markets, but doesn't quite drown the U.S. government)

 

[FIRE'd@51]

In fact, you can imagine the limit, as N goes to infinity,
of this expression; I'm a little rusty on how to compute the limit, but
you could approximate it with N=1,000,000, and it's still 5.127%

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%

 

[saluki9]

Thanks Fire'd I thought I was going to have to go through the whole natural log thing

 

[HFWR]

Not to nitpick, but shouldn't it be:

=((1+.0508/365)^365)-1 = 5.21%

Well, you do have to enter it into a calculator this way...

 

[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

 

[justin]

Well, you do have to enter it into a calculator this way...

What kind of calculator? My TI graphing calculator and excel formulas don't require the second set of parenthesis. They both use the standard order of operations (PEMDAS).

 

[justin]

You learned that in 4th grade? You must have gone to school with JG in the advanced section.

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)

 

[HFWR]

I went to college before graphing calculators...

 

[Martha]

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.

 

[bosco]

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!

 

[Nords]

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?"

love RPN!

I was wondering when that would come up. It's the mathematics equivalent of Godwin's law...

 

[JohnEyles]

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 ?

 

[FIRE'd@51]

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