Archives for May 2006

In my previous post on Calculating and Comparing Treasury Bill Returns, it was pointed out that my APY calculation was incorrect because the way T-Bills work, you can’t actually reinvest all the interest into the next T-Bill. That is true, but what you can do is set your T-Bill to fund and deposit via another interest-bearing account like Capital One Consumer Bank, Emigrant Direct, or HSBC Direct. This way, you can still invest in consecutive 28-day T-Bills, and anything not rolled over to the next T-Bill is still earning decent interest.

But, we still want to compare APYs! So, what was needed was a calculator that would take all this into account. So here it is:

28-Day T-Bill APY Calculator:

Principal invested per $1,000 par value: $.

T-Bill interest earned: $
Bank interest earned on excess interest: $
The approximate total APY is: %

Example
Let’s do an example. Let’s take the most recent T-Bill results for a $1,000 28-day T-Bill and say you set it to reinvest every 28 days. The investment rate is 4.655%. Now, let’s say you fund via Emigrant Direct, currently at 4.50% APY. Using the APY to APR calculator³ and the fact that ED compounds daily, we get an APR of 4.401%.

We input these values above. It spits out that for each $1,000 T-Bill you buy, you’ll pay $996.43. Actually, you’ll pay $996.44, but that’s due to rounding errors². No big deal.

So when you buy a 28-day T-Bill, $996.44 will be taken out of your Emigrant on the next Thursday after the auction you participate in.

28 days later on another Thursday, your ED account will get a deposit of $1,000 and also a withdrawal of $996.44. $3.56 cents is left behind and earns interest at Emigrant. 28 later again, the same thing happens. Another $3.56 is left behind. This continues for a year and 13 T-Bills⁵ mature in that 364 days. At the end of this theoretical¹ year, you’ll get approximately ($46.38 from T-Bill + $0.95 from Emigrant =) $47.33 in interest from your $996.44 initial investment. That’s an approxmiate APY of 4.75%.

It’s not perfect, but it’s something more accurate than investment rate that you can now use to compare with other online bank APYs. Note that this is pretty close to the APY that would be calculated assuming full interest reinvestment – 4.76%.

Finally, this does not take into account the tax benefits of T-Bills for those that are in states that charge state or local income taxes.

Assumptions and Caveats
1) The calculator assumes that the current T-Bill rate is extended out for an entire year. This cannot happen in real life as the rate is determined by auction every week. We are just extrapolating to find APY for comparison purposes. Banks change rates throughout the year as well.
2) There are plenty of round-off errors since I am allowing you to input the investment rate, which is already rounded off.
3) I again note that I am asking for the APR of the savings account you will be using, not APY. Hence, my APY to APR Calculator.
4) I am assuming that the bank interest compounds every 28 days for simplicity. Some banks compound daily, some compound monthly. It really doesn’t matter that much.
5) In actuality, there are 13.0357 (28×13= 364) T-Bills.