I’ve been getting a flurry of questions about comparing Treasury Bills to bank accounts. Here is a step-by-step walkthrough to make it from the weekly auction results to a bank’s quoted APY interest rate.

**1. From the recent auction results page, grab the investment rate ( not discount rate).** This is APR. It is based on a 365-day year and reflects the actual annualized rate to maturity. Here’s the most recent snapshot:

Let’s take the 28-day T-Bill, which has an APR of 5.247%, or 0.05247.

(If you want to learn more about how the other terms and the relationship between “Discount rate” and “Investment rate”, please see this post on T-Bill terms.)

**2. Convert it to APY.** APY, as opposed to APR, takes into account the effect of compounding interest. It’s also a higher number, which is why most banks just tell you the APY. An approximate way to convert it to APY is using this formula:

APY = (1 + (APR/PeriodsInAYear) )^(PeriodsInAYear) – 1

For our case, the APR is 0.05247 and PeriodsInAYear= 365/28. Solving for APY, you get 0.05376, or **5.376% APY**.

This is only a approximation because you can’t actually reinvest *all* of the money continuously. For example, you might get back $1,000 from your first T-Bill, but can only reinvest $995 of it in the next T-Bill. The rest must sit in a savings account at best. For 28-day T-Bills, you can get a more accurate number using my 28-Day Treasury Bill APY Calculator.

Assuming a 4.89% APR/5% APY savings account, you’d get **5.367% APY**, a bit less. If you don’t pay state or local income taxes, you can stop here. As you can see, it’s very competitive with online savings accounts.

**3. Find Your Tax-Equivalent Rate.** Treasury Bills are exempt from state and local taxes. Thus if you are subject to such atrocities ;), then your T-Bill rate is actually better than that of a fully-taxable bank account. This is one use for my tax-equivalent yield calculator. You’ll need to know your tax rates and whether you itemize taxes.

Let’s use the 5.367% number from Step 2 and my own tax situation. For 2007, I’ll probably be in the 28% bracket federally, 9% for state, and will itemize. For this specific T-Bill, my final number that I should use to compare to banks is **5.898% APY**. Your number will probably vary.

Yes, there are a lot of variables to get the conversion just right. Sorry!

If you are interested in investing in Treasury Bills, please also see my visual guide to building a T-Bill ladder to maximize your returns and also liquidity.

Thanks for your posts re T-Bills. I got started on them late 2006 because of this site! It’s nice to earn a little more interest $$ than my online savings accounts, at the same time saving a little on state taxes Take that, NJ taxman!!

Thanks for this post!

Jonathan,

May I ask you a state tax question regarding these 28-days t-bonds?

As your loyal reader, II did several purchases through treasurydirect.com. But when I prepared 2006 tax by TurboTax Deluxe (State: California), I don’t know where I can exempt state tax for these interests.. Any suggestion or idea??

Jonathan,

You can also mention that If one itemizes but is subject to AMT then the effect of itemization should not be included in the calculation because AMT means you dont get to deduct extra state taxes from federal income.

I like to do the calculation just using the APR myself, since I know I’m likely to set it up from my checking account and not immediately reinvest the T-Bill dividends. It can still yield a compelling rate of course.

I never knew that T-bills are exempt from state taxes… probably not a big deal since I have never owned any.

One thing that I did want to say is that I searched the site for information regarding municipal bonds and found very little information. If you’re looking for tax savings vehicles, these are even better than T-bills because they are exempt from federal and state income taxes (provided your bonds are issued by your municipality). For instance, I live in MD and own shares in a MD muni bond fund. My federal tax bracket is 25% and my state bracket is 8% for a total of 33%. The fund yields 4.5%, which is equivalent to a taxable yield of 4.5%/(1-0.33)=6.716%. Of course, I am sure you are aware of all of this, so my real question is why haven’t you shown much interest in this possibility?

First of all, this is my first post here, I enjoy your blog very much. I got here looking for information on T-bills and not the other way around

I just can’t figure out how the 5.247 is obtained… bare with me for a second.

If one does the math as in the other post

APR = (return per $1)*365/28 =

= (100-99.646889)/99.646889 * 365/28 = 4.6194% –> round to 3 decimal places

For these latest results,

APR = (return per $1) * 365/28 =

=(100-99.600222)/99.600222 * 365/28 = 5.2323% –> difference in the 2nd decimal place

Other comment with respect to the other post (as it relates to the numbers I wrote above).

If you buy a $1000 bill for 996.47, thus getting

$3.53 of interest, I would think that

(return per $1) = 5.53/996.47 = 0.003542505,

instead of the .00353 posted

I know the difference seems small, but there is quite a lot of error in this equality

“.04619 x 28 days/365 days = $0.00353 “,

it would be more like 0.04602

just wondering

silvia – Writing this up right now.

MM – I’m sure you’re right. I am not well versed at all with the dreaded AMT. I secretly hope that it will get repealed or “fixed” before I am affected by it.

Don – Yep, perfectly good idea, it’s all about apples-to-apples.

Chris H – I haven’t shown must interest in such municipal bonds because (1) I am moving to a different state soon and muni bonds tend to have pretty long terms and (2) they can be difficult to invest directly in. There are some great municipal bond mutual funds for certain states, but not Oregon. (They exist, but the performance and expenses make them undesirable.)

bm – It’s all rounding errors. Your 99.xxxxx is a rounded number. The only number on that chart that is exact is the discount rate. Trying getting the ENTIRE 99.xxxxxxxxxxxxxxx… on a computer or nice scientific calculator from the first equation, and re-run the numbers.

I think the reason they give a “Price per $100″ instead of just $996.00 is that if you buy a $1,000,000 T-Bill (not unheard of by large institutions or foreign countries, they won’t just charge you $996,000, they’ll charge you 996,002.22. If someone wants to try and report back, that would be greeeeeeeat.

Okay, I take that back – I just ran the numbers myself and got the same number…

APR = (return per $1) * 365/28 =

=(100-99.600222222222)/99.600222222222222 * 365/28 = 5.232306…%

At this point, I’m stumped! Anyone dare ask the Treasury to back up their numbers?

A very smart reader KS figured it out: Try using 366 days as the year instead for all dates after 3/1/2007. There are 366 days from 3/1/2007 to 3/1/2008.

Jonathan:

Use 366 days in your calculation instead of 365 and it works fine. This is true for all issue dates 3/1/2007 onwards. I figure the treasury uses the one year period following the issue date which for 3/1/2007 onwards would include 2/29/2008 (the “leap day”). For issue dates prior to 3/1/2007, 365 days gives the correct investment rate.

Per the Treasury website. The seem to be using a 360 day year.

“Treasury Bills

* Treasury bills are short-term securities maturing in one year or less.

* Bills are sold at a discount from their face value.

* When a bill matures, the investor receives the face value.

* The difference between the purchase price and the face value equals the interest earned.

For example, if a $1,000 26-week bill sells at auction for a 3.80% discount rate, the purchase price would be $980.79, a discount of $19.21. The purchase price can be determined from the following formula:

P = F (1 – (d x t)/360), thus

P = 1000 (1- (.0380 x 182)/360), solving

P = $ 980.79 “

This should be added to the earlier post.

P = Price

F = Face value

d = rate of discount

t = days to maturity

Jonathan, KS,

thanks, that is the ONE thing I did not think about… I can stop scratching my head now 😉

The question to me now is whether or not banks adjust their APY/APR numbers accordingly? Not that it makes a lot of difference…

Jonathan — love the blog.

Just a quick comment about municipal bonds. Not all municipal bonds have long maturity dates. For those who DO want to go the Muni Bond route, but want quick access to cash, you should consider a Daily or Weekly Municipal ARS (Auction Rate Security) product. The rate on these bonds is determined through a Dutch-auction process — much like T-Bills and other Treasury-issued securities.

Minimum investment in a PARS product is usually $25,000 with $5000 increments. They come in daily, weekly, and monthly auctioning varieties. Your broker will automatically roll your bond to the next holding period if you don’t wish to sell; however, if you wish to sell, the broker will buy it back at par and you can get cash. Therefore, if you buy a daily, you can put it back to the broker for cash any day you want…at par. You must submit your sell order before the auction deadline for your broker (usually 10am or so).

Check out http://www.bondmarkets.com/story.asp?id=1882 for indices that show some benchmarks that should give an idea on how these perform. Note that because of the demand for paper issued by high-state-tax-states (i.e. CA, MA, NJ, NY), the price goes up, meaning the yield goes down. However, as of this post, the index rate for a non-specialty state weekly product is 3.57%. At 28% federal tax rate and 5% state tax rate, this works out to be a 5.37% equivalent taxable yield.

Note that I am not a banker, nor a lawyer…but I work for one.

I can’t figure out how you got 5.898% from 5.376.

=5.376%/(1-0.28-0.09) = 8.53%.

Can you pls explain? I am in NJ and both Fed and State exemption can be taken.

Thankyou.

Jonathan, have you had any chance in opinion on T-bils? Recent auction results (6/21) for the 28-day T-Bill is only 4.335% discount rate vs the 5.14% in your example above? The lower rate on recent results makes the T-Bills less attractive than say a 5.25% ING CD even with tax breaks considered.

I’ve stopped buying T-Bills, mainly keeping everything in FNBO Direct at 6% for now. Also looking at some municipal bond options recently, but haven’t really figured it all out yet.

One thing I’m trying to figure out in treasury bill investing is how to factor in the state/local and federal capital gains tax on the difference between your purchase price and the face value recieved at maturity. For example, if you buy a discount T-bill at 97.500 you are obligated to pay tax on the short-term capital gain from your $2.50 appreciation in the bond value (which redeems at $100). This will drop the effecive yield and make it less competitive or perhaps even worse off than a CD. Thoughts?

Kevin, that $2.50 earned in your example is not a short term capital gain. You just bought it was $97.50 and earned interest. You did not “sell” it at $100.

The Treasury will make a 1099 in this regard.

Hey Jonathan,

I had a question for you. It’s been a while since you’ve mentioned the treasury bill. And back when this was posted rates were great! But now with the market down the shoot, and rates hovering around 1.84% on the high side, I was just wondering, do you still do this? I know there are banks out there, I just opened up one that 3.75% APY compounds daily. I’d be losing serious money if I did this now. Maybe in the future though. Just thought I would ask for an update since it doesn’t seem like much sense now.

No, I currently do not own any T-Bills, and let my ladder lapse. There are much better rates from retail banks currently for no-risk cash.

The links here are broken to the T-Bill historical rates. The correct location is now:

http://www.treasurydirect.gov/RI/OFBills

Hope this helps.

Fixed, thanks.