I am sure this is very simple, but I can't figure it out: I am trying
to figure out if I would get a better return investing in a 3-mth
T-Bill or leaving my money in an online savings account like ING
Direct or Emigrant Direct. In your answer, don't just tell me which is
better, but how to compare the interest on the T-Bill to the APY of
the online account. Thanks!

To compare interest in a T-Bill purchase
(http://www.savingsbonds.gov/indiv/research/indepth/tbills/res_tbill.htm)
or a online savings MMA
(http://www.bankrate.com/brm/rate/chk_sav_home.asp), let's take a
hypothetical example.

I have $10,000.

Option 1
-----------
Buy T-Bill online through treasury department.  Rates are set at
auction.  Because of our non-instiutional-sized purchase ($10,000),
our rate is non-negotiable/non-biddable.  Rates are published here
(http://wwws.publicdebt.treas.gov/AI/OFBills).
The 12/15/05 auction is selling 91-day notes at $99.034389 to mature at $100.
$10,000 would then buy 100.975025 T-bills.  (10,000/99.034389). 
100.975025 T-bills X $100 face value = $10,097.50 or $97.50 in
interest collected at the end of 3 months.

Option 2
------------
Place $10,000 in online savings account. Rates vary and can change
month-to-month, but for comparative purposes, let's take the
prevailing rate.  It's only 3 months and any increase/decrease can be
offset by the value of the liquidity of this investment.  Rates
available at bankrate.com.

$10,000 at 2.50%APY for 1 months = $10,000 X (.025/12) = $20.83
$20.83 X 3 months = $62.50

In these 2 options the T-Bill yielded a better return. $97.50 vs $62.50
(PS, this doesn't take into consideration that a T-Bill is exempt from
state & local taxes, another T-Bill plus!)

---------------------
Now I suspect you want to compare apples to apples, rate to rate.  The
problem is the frequency in the compounding of interest.  You can't
take the published discount rate published by the gov't on T-bills and
compare it to the APY of a MMA because this rate isn't APY.  See
discussion:


(http://bankcd.com/question.html#What%20is%20the%20difference%20between%20APR%20and%20APY)

APR (Annual Percentage Rate) is simple interest without compounding.
For example, $10,000 @ 6.00 APR for 2 years will produce $600 of
interest per year (or $300 semiannually, or $150 quarterly, or $50
monthly). APY (Annual Percentage Yield) is compounded interest
(usually daily or monthly) calculated for 1 year (even if the term is
longer). For example, $10,000 @ 6.00 APR for 2 years compounded
monthly, produces a 6.17 APY which returns a total of $11,272.07 after
2 years. For comparison purposes, banks often quote the APY of
investments that don't compound interest. This is interpreted as "if
the interest were to be compounded, this would be the APY".

--------------------------
If you have any training with a financial calculator I would just plug
the security "terms" into the PV, n, R, and PMT functions to determine
a FV and the best investment option.  Or, just run a generic
investment through the terms to compare.  OR... here's the scoop:

(http://www.in-the-money.com/glossarynet/Treasury.htm)

-----------------------
For our example use this formula on T-Bills
(100/Price)^(365/daystomaturity) - 1 = Approx APY
100/99.034389^365/91 - 1 = 3.97% Approx APY

Treasury Bills are exempt from state and local income taxes (not
federal). For comparison you need to take into account those
tax-advantaged with the regular interest rates from a bank savings
account or CD. The formula to find the equivalent bank rate that gives
us the same after-tax return.

RateBank * (1 - Fed Tax Rate - State/Local Tax Rate) =
 RateTBILL * (1 - Fed Tax Rate)

This gives us:
For a given TBILL rate the equivalent from the regular bank would be.

RateBank=RateTBILL*( (1-FedTaxRate)/(1-FedTaxRate-StateLocalRate) )

Example if Treasury Bill is paying 3.696% and federal tax rate of 28%
and a state tax rate of 10%. This makes the equation above:

RateBank = (1-0.28)/(1-0.28-0.10)* RateTBILL

(Equivalent) RateBank = 1.161 * 3.696 = 4.292%.

Overall, the higher your federal and local tax rates are, the better
off you are with tax-advantaged investments from the U.S. Treasury,
although it is much more sensitive to state and local tax rates.

As pointed out, this equation assumes that you are not deducting your
state taxes on your federal taxes. I won't get into that because it's
hard to say exactly how much more you are getting when you take into
account that everyone gets the standard deduction anyways.

Source:
http://www.mymoneyblog.com/archives/2005/10/finding_the_equ_1.html

Based on my tax situation the recent auction results makes the Online
Savings account even with T Bills.

Keep an eye on the results weekly to see the trend at 
http://www.publicdebt.treas.gov/of/ofaucrt.htm


Regards,
Denis