T-Bill Investment Rate: Is it APR or APY? And What Is Your Taxable Equivalent Yield?

If you go to TreasuryDirect’s website and check the latest T-Bill rates, you will find a table with the following seven columns: Security Term, Issue Date, Maturity Date, Discount Rate %, Investment Rate %, Price Per $100, and CUSIP. As a 4-Week T-bill investor, when I look at the table, the single item that concerns me the most is the Investment Rate because that determines what I will get in return when the bill matures in 28 days. For the bills issued on November 2, 2006, the investment rate is a very solid 5.176%. And that rate alone makes T-bill the best short-term investment choice (with the only drawback of a 28-day holding period).

The best?

But I can get a 5.50% APY from E-Loan with a $5000 deposit and that must be better than the 5.176% rate of the 4-week T-bill!

True that you can get 5.50% APY from E-Loan, but T-bill still offers you more than what you think because the 5.176% investment rate of the most recent T-bill is APR instead of APY. For the sake of fair comparison, you have to convert APR into APY, otherwise you are comparing apples with oranges.

To see why 5.176% is APR instead of APY, you need to know how that rate is calculated. If you go back to the TreasuryDirect table, you can find a column called “Price Per $100.” Since T-bill is sold at discount, the price you pay is less than its face value and if you hold the bill to maturity, you will receive the face value. For T-bills issued on November 2, you pay $99.6045 when you buy the bill and receive $100 on November 30 when the bill matures. And the investment rate is calculated with this price using the following formula:

Investment rate = (100 – Price Per $100)/(Price Per $100) * 365/28

For the price of $99.6045, the investment rate is

Investment rate = (100 – 99.6045)/99.6045 * 365/28 = 5.176%

Since the above formula doesn’t consider any compounding of interests, the investment rate is just a rate (APR), not a yield (APY).

So what’s the corresponding APY of the investment rate of 5.176%? Using the following formula:

APY = (1 + APR/(365/28))^(365/28) – 1

to take into account the effect of interests compounding. For the APR of 5.176%, it works out an APY of

APY = (1 + 0.05176/(365/28))^(365/28) – 1 = 5.302%

That’s still almost 20 basis points shy of the 5.50% APY E-Loan offers. But you have to know that interests earned from T-bills are exempted from state income tax (not federal tax though). Taking this into the calculation, the taxable equivalent APY becomes

EAPY = APY/(1 – State tax rate)

Since I am living in NJ and the state tax rate for me, according to Salary.com, is 6.37%, my equivalent APY is

EAPY = 0.05302/(1 – 0.0637) = 5.663%

beating E-Loan by 16 basis points! And the higher the state income tax rate, the higher EPY.

Of course, as mentioned earlier, buying T-bill will tie your money for 28 days, while with E-Loan you have the full liquidity. But you do have to have $5000 to just open an E-Loan account. With TreasuryDirect, the minimum purchase amount is $1000 and if you buy $1000 each week for four weeks (28 days), you can build a T-bill ladder with repeat purchases.

Check out my previous post to see how to set up repeat purchase at TreasuryDirect. Fatwallet has a nice discussion on Treasury bills and here is an online spreadsheet to calculate your EAPY.

Update: The above EAPY is assuming you itemize when filling your federal tax returns. An update is available here for non-itemized returns.

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16 Responses to “T-Bill Investment Rate: Is it APR or APY? And What Is Your Taxable Equivalent Yield?”

  1. John |  Nov 06, 2006 at 4:56 pm

    Thanks for the t-bill lesson. There is one more positive thing about a t-bill compared to a fixed rate savings account. A fixed rate savings account is subject to federal and state taxes. So that 5.5% APY is is even lower after uncle sam takes his cut. I’m not sure how to calculate it, but it’s probably somewhere around 5%.

  2. The Sun |  Nov 06, 2006 at 9:36 pm

    You are absolutely right, John. The taxation actually makes the offer worse than it appears. However, we usually don’t think about taxes as we have to pay them no matter what kind of deal we get.

  3. goldsheet |  Nov 07, 2006 at 6:31 pm

    Your EAPY formula is correct if you itemize, but for non itemizers the federal marginal rate comes into the calculation as follows:

    EAPY = APY * (( 1 – FedTaxRate) / ( 1 – FedTaxRate – StateTaxRate))

    The result will be an even higher rate than the 5.663% you calculated. This is discussed on the FW thread, and the above formula is in the spreadsheet. I know because I am a victim of the 9.3% CA marginal rate and update the CA equivalent rates in the FatWallet Quick Summary.

  4. The Sun |  Nov 08, 2006 at 9:48 am

    Hi goldsheet:

    You are absolutely right. The EAPY I gave is only for itemized deductions as I thought most people will indeed itemize.

    Thanks for pointing it out and I will update the entry shortly.

  5. Chris Duncan |  Dec 21, 2006 at 5:37 pm

    Good information. For short-term investing seems like a better deal, what about longer term investments? Seems like the yields on CDs for 1Y and longer beat the treasury even when you take into account taxes.
    CA TEY on the 2Y is 5.13. Still good CD rates 10 – 20 BPs above that.

  6. The Sun |  Dec 22, 2006 at 12:30 am

    While it’s true that longer term CDs offer better rates (taking into consideration of federal taxes, 1-year CD rate may actually lower than that of the T-bill), it’s not really fair to compare them with 4-week T-bills as 4-week T-bills only tire your money for 4 weeks instead of 1 year or even longer. The short-term T-bills are supposed to be used as an alternative to the regular savings accounts. To get a higher rate, you have to give up the flexibility.

  7. Erica |  Mar 28, 2007 at 11:12 pm

    I’m just learning about T-Bills and appreciated your website. I do have a clearification question. Is the interest earned from T-Bill investment subject to federal taxes?

  8. The Sun |  Mar 30, 2007 at 12:32 pm

    Erica: Yes, interests earned from T-bill investments are subject to federal taxes, but not local and state taxes. Therefore, when you compare various short-term investment choices, you have to factor in this to get an idea where the interest rate stands.

  9. Paul |  Mar 31, 2007 at 7:38 pm

    Thank you very much guys for such a useful detailed review. I built up a little asset on my savings which is $10K+. From what I read I estimated if I invest $10000 in T-Bills I will collect around $30-$40 at the end of the 28 day period. Here comes my question: do you think $10K is enough to benefit significantly from T-Bills ? Or maybe I am not calculating anything correctly ? As for me $40 a months is not worths the trouble. What amount, do you think, one should have to start investing in T-Bills?

    Thanks a lot!
    Paul

    Thanks in advance,
    Paul

  10. The Sun |  Apr 01, 2007 at 8:47 pm

    Paul: I think your calculation is fine. With current rate of 5.24% APR, you will get about $40 at the end of the 28-day period for $10K. However, whether this is a good choice can’t be determined by one single number. Instead, you need a comparison. In absolute value, $40 may be small. But it could well be a better choice if you compare T-bill with other investment choice. What are you going to do with th $10K if you don’t buy T-bill? Put it in the bank? If so, what’s your interest rate? Or you may want to invest it. If this is the case, then you may not have $10K after 28 days.

    So can you share with me what’s your choice other than T-bill?

  11. Paul |  Apr 01, 2007 at 10:56 pm

    Dear Sun, thank you very much for your fast response. Let me tell you a little history. I saved around $10K+ in my saving and learned that my CU APR is around 1.4%. This is ridiculous to seep money in the bank with this APR. I started doing some research and learned about Money Market, CD, and T-Bills. Money market is OK, APR/APY isn’t to high though. CD are unacceptable for me because:

    1. Liquidity is lost for 10-14 months
    2. I can get the same outcome from online saving accounts (HSBC or EmigrantDirect, etc…)

    Definitely I am putting my money into eBanks. I was looking for another options. As far as I understood T-Bills will give me the same outcome as eSaving (savings online) then why to trouble myself with T-Bills?

    Well, let me know your thought, which will be greatly appreciates. What would you do with $10K+? I did some googling online and just got a few silly suggestions like to treat myself with a flat screen TV. Let me tell you a secret, I am not an American and money doesn’t burn my pocket. I am just looking into different options. Let me know! And thanks a lot in advance!

    AKA Paul

  12. Sean |  Jul 18, 2007 at 12:55 am

    Paul raised a very good question. Would like to hear some feedback on his question.

    Sun,
    Thank you for keeping such an informative blog. I’ve spent hours on your site learning as much as I can.

    Appreciatively,
    Sean

  13. Sun |  Jul 18, 2007 at 9:51 pm

    Paul & Sean: It doesn’t matter which investment/saving vehicle you are using, the ultimate goal is to make the most of your money. For savings accounts, my money always go to the one that pays the highest rate. This is also true for T-bills. If the T-bill rate (the effective yield after you factor in your state income tax rate) is identical to that the rate of an online savings account, there’s no reason to favor T-bill over a savings account. I have stopped buying T-bills for more than a month and I have no plan to jump back in if the rate stays at current level.

    If I have $10K, I will definitely invest it. Then where to invest the money depends on when you will need the money. If you will use it in, say, 2 to 3 years, buy a long term CD may be the best choice. If the money is for your retirement or that you won’t touch in 10 or 20 years, then investing it in an index fund or ETF in lump sum makes more sense.

  14. alan |  Jan 12, 2008 at 11:57 pm

    am i crazy for looking for a 7-8% return, is there such a thing, that is safe? there is a bank, mlnbank.com, millenium bank i think that is offering 8% long term cds. For real, or pipe dream?

  15. Steve |  Jan 14, 2008 at 4:38 pm

    I have a traditional CD which yields 5.1% APR – I think. It is locked for 9 months – lets just say I have 10,000 to invest. Would it make more since to invest in t – bills or just keep it in the traditional CD

    thanks

  16. Sun |  Jan 23, 2008 at 10:28 pm

    Steve: To consider whether investing in T-bills still makes sense to you, you need to calculate your equivalent yield of the T-bill because the T-bill rate given by the Treasury is APR that doesn’t not include state income tax. To do the calculation, you need to covert APR to APY first then get the yield corresponding to your state income tax rate. Given the current rate of T-bills, I am afraid it won’t make too much sense to invest in T-bills. Locking in a higher rate CD before the rate falls again may be a better option.