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.

Note: 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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