# Equivalent Interest Rate For T-Bills / Savings Bonds Calculator

I whipped out my ancient how-to-make-a-website book, and made a simple but handy JavaScript calculator for calculating the equivalent bank CD rate for a given T-Bill or Savings Bond rate, as the interest from them are exempt from local and state taxes. This uses the rate conversion formula previously given. Remember, marginal means the tax rate at which your last earned dollar is taxed. Please try it out and let me know if something’s broken:

Calculator:

Enter your marginal federal income tax rate:
%
Enter your marginal state/local income tax rate:
%
Enter the T-Bill or Savings Bond interest rate:
%

The approximate equivalent bank rate is:
%

For example, at my 25% Fed and 9% State tax rates, the current 4.14% rate for a 4-week T-Bill is the equivalent of a 1-month bank CD earning 4.70% annualized.

Note: The above calculator does not assume that you will itemize deductions and deduct your state taxes from your federal taxes. Even if you do itemize, I would note that everyone gets the standard deduction, so it’s not necessarily fully deductible.

Useful Resources:
Recent T-Bill auction results
2006 Federal Tax Rates
State Income Tax Rates

1. How is the T-Bill rate calculated? I purchased a 4-week T-Bill for \$1000. The rate was 4.033% according to the TD site. The purchase price was \$996.92. So I will receive \$3.08 at maturity. At an APR of 4.033%, should the purchase price have been \$996.39 and I should recieve \$3.60 at maturity? I can’t seem to get the calculation right.

2. Dan says:

Jonathan – I really like the calculator!

Steve – I think I may have originally been making the same calculation mistake – thinking of the 28-day bills as “1-month” bills, and therefore dividing the rate by twelve to determine the interest at maturity. But with all of the 30- and 31-day months, it’s actually quite close to 13 4-week bills you can reinvest within a year’s span. So I think you’ll find if you divide by 13 instead of 12, the number will come out very close to the investment rate the Treasury has posted.

(Or if you really want to be as precise as possible, divide by 365 and then multiply by the number of days in the term of the bill to get the interest.)

3. That was my problem. Thanks Dan!

4. john says:

Your calculator does not work. If you goto CNN web page and use there calculator you get a yeild of 4.55% and I think CNN knows how to program there web page correctly.

http://money.cnn.com/pf/101/lessons/7/page4.html

5. Ashoro says:

Jon, I have a question :O… or anyone who can answer it… If I’m not working, how much interest am I allowed to make from my savings before having to file taxes for it?

6. john, I would have to disagree with that calculator. It’s not quite right. You would not be getting the same after tax returns.

For example, if you were at the 25% Fed rate and 9% State rate,

1) For a \$1000 T-Bill earning 4% interest, after a year you would get \$40, subject to only 25% tax.

Result: \$30 after tax

2) \$1000 bank CD

My calculator result is 4.545%. That would give you \$45.45, subject to 25+9= 34% tax.

45.45 * .66 = \$30.

CNN’s calculator result is 4.40%. That would give you \$44.00, subject to 25+9= 34% tax.

44 * .66 = \$29.04. (close, but not quite).

If I’m wrong, at least show me why you think so.

7. Ashoro – Interest income is income. If you had to file taxes anyways, you legally must report all interest income. Whether the IRS will come after you is a separate question.

8. Ashoro says:

Oh thank you, 1 more question:
The whole taxes on gifts from parents, whether it is 11k or 12k, say if my dad sent me 13k (which was originally meant to pay for tuition which would be exempt but now I got loans so it’s not…), it still wouldn’t be taxeable right? Because the extra amount of 1k or 2k simply becomes income and is too little to be taxed to matter for someone not working?

9. Jim says:

Jonathan, I am not quite sure why your results are different than CNN’s, but it might be because CNN assumes you can deduct state tax on federal filing? Then your tax would be (0.25+0.09-0.25*0.09)=0.3175

then 44*(1-0.3175)=30.03, close enough?

10. Hmm… maybe, good point. Like I’ve said before, I think doing that overestimates the advantage of being able to deduct your state taxes on your federal taxes.

1) To do that, you must itemize deductions. Many people do not itemize.

2) Even if you do itemize, the tax advantage of itemizing is only that which exceeds the standard deduction. This is also why some people overestimate the usefulness of the mortgage interest rate deduction.

The standard deduction for 2006 is \$5,150. Say if you itemized and get \$10,000 in deductions. Only the amount above the standard deduction, \$4,850, actually saved you any money. So you could either look at the first half of your deductions as totally useless, or pro-rate the effectiveness of each individual deduction. I think the latter makes more sense.

But hey, it’s not that big of a difference overall. And I don’t itemize, so I won’t sweat it. =)

11. To Jonathan’s comment above. The standard deduction/itemized deduction can be teamed up to save you even more money.

For instance, let’s say you pay tithing every year (tax deduction) of \$7,000. That means you were able to deduct an additional \$1,850 above the standard deduction. You paid less taxes.

If you did that for 6 years you would have deducted \$11,100 MORE than the standard deduction allowed (assuming it stayed constant, for sake of calculation).

However, what if you bunched your tithing and pre-paid it when fitting?

Year 1: You pay \$7,000 at the beg. and \$7,000 at the end of the year (\$14,000 total).
Year 2: Take the standard.
Year 3: Double up again.
Year 4: Take the standard.
Year 5: Double up again.
Year 6: Take the standard.

Instead of having total deductions of \$42,000 (\$7,000 * 6 years), you have total deductions of \$57,450 (\$14,000 * 3 years + \$5,150 * 3 years).

Whenever you’re borderline itemized, it often makes sense to shift some deductions to the next year and take the standard.

12. Eric says:

The gift tax which you (ashoro) are referring to, is paid by the giftor (the one giving the money) not the one receiving the gift.

TO Jesse, your correct – and that’s what most seniors will do to with things such as property taxes. 2001 they don’t pay, 2002 they pay both years amounts for a itemized deduction, 2003 nothing, 2004 they once again pay double – etc. It really all depends on your situations but the key word here is “planning”. You have to plan for these such things and make your best educated ‘guess’ as to what would be best.

13. nick says:

why does you tax equivalent calculator take fed taxes into account? TBills are federal taxable. Or am i missing soemthign?

14. I know it’s counter-intuitive, but it has to do with the fact that you’re trying to find the equivalent fully fed- and state-taxable bank rate and you’re working backwards to get it.

15. Scott says:

Sorry if this has been asked before — I’ve tried to read your other posts on T-bills…

Wouldn’t you want to convert the T-bill’s “investment rate” into the corresponding APY before comparing it to a commercial CD’s APY? I know you wouldn’t actually get the resulting APY on the T-bill b/c you don’t know the rate at which it would renew, but the same is true for a 6mo CD. At least this way you’d be doing an apples-to-apples comparison.

16. KingSideRook says:

I’m a bit late to this party, but anyhow… The reason Jonathan’s calculator produces somewhat incorrect results (as opposed to CNN’s) is that Jonathan used substraction instead of division in his formula. It’s an approximation that many people use but the exact formula should be:

bank_rate * (1-fed_tax) * (1-state_tax) = bill_rate * (1-fed_tax)

from here we get:

bank_rate = bill_rate / (1-state_tax)

17. As I’ve stated in the post where this formula was derived, the reason for differing formulas is that other formulas assume that people are deducting their state taxes from their fed taxes. Not everyone does that.

Everyone gets the standard deduction, so you are overestimating the benefit of that. My formula should be accurate for those who don’t itemize and errs on the conservative side for those that do.

18. KingSideRook says:

After spending a few minutes playing with the math I realized that you are correct. Thanks, Jonathan!

19. Ross Murphy says:

Can someone help me with this one please? Suppose someone lends an off-shore company, incorporated in Malaysia, \$2000. The Malaysian company invests the money in US T-bills. The company pays no US taxes. The investment period is 90 days. How often is interest calcualated during this period?
I was told that a T-bill pays compound interest every six minutes. If this is not so, what is the correct periodicity? If it is something else, what is it, and the most important question is, how much is earned in 90 days, 180 days or one year?
Thanks so much for any help or clarification.
Ross Murphy, Shawnee, KS

20. Jim says:

I have \$50,000 I would like to invest in 28 day t-bills, could you tell me what my investment would have brought from the last t-bill auction.

21. Ames Tiedeman says:

In the U.S. interest rate are going lower, Gold is going higher, Oil is going higher, inflation is going higher, the dollar is going lower. What is wrong with this? Everything! At some point the FED is going to have to raise rates bigtime. We are in a very, very, precarious situation at the moment. I think Gold will tripple to over \$2,000 an ounce when the market finally wakes up and sees the real inflation. Last I checked a lower dollar = higher import prices. There is no inflation deflator here. With commoditioes on fire you can forget about that. Bernanke should have never lowered rates last week. However, the Fed might be doing something that few have talked about. Maybe the Fed has abandoned the dollar to crush the trade deficit. Good luck, it will take 20 years to correct our 6% of GDP trade deficit and move it back to under 1% of GDP, unless you want to seriously disrupt the global economy. We are in for tough times people. Very tough! The FED will not be able to save housing with lower rates. We are in for a 10 year decline in home prices. It is called a cycle!