The imputed interest rate on a T-bill. As discussed earlier, T-bills are issued at a discount off their $1,000 par value, not quoted as a yield. To determine that yield, you need to know the price and the number of days to maturity. For simplicity's sake, a year is considered to be 360 days long, which assumes there are 30 days in a month. (This day-count convention may actually make things more complicated, but the 360-day year is now a tradition for calculating T-bill rates).

Computing a T-bill's discount yield is a three-step process. For these purposes, carry all computations out to six digits to the right of the decimal point. Treasury's mainframe carries it out 15 digits.

  1. Subtract the price you paid for the bond from $1,000. Take the difference and divide it by 1,000. Let's say you are buying the bond for $999.38. Subtract $999.38 from $1,000 and divide the resulting $0.62 by 1,000, and you end up with $0.000622.

  2. Now you take 360 - the number of days in a year, by convention - and divide that by the days to maturity. Let's assume it is a one-month bill, which usually matures more precisely in 28 days. Now divide 360 days by 28 days for a result of 12.857143.

  3. Now you multiply the result of step 1 by that of step 2. $0.00062 times 12.8571 equals 0.8%.

Look Out!
Do not get thrown off by orders of magnitude. A percentage is a number divided by 100. Do not think of 0.8% as 0.8%, but rather as 0.008. Sometimes bond traders refer to "basis points" or "BPs" or "beeps". A BP is a hundredth of a percent, or a percent of a percent. Maybe it will help you to think of 0.8% as "80 beeps".



You also need to be able to do this backwards. Given the rate, can you figure out the price?

  1. Multiply the rate by the number of days to maturity. In this case, multiply 0.008 times 28 days, and your result is 0.224.

  2. Divide the result of step 1 by the conventional number of days in a year. In this example, that would be 0.224 divided by 360, which gives you 0.0006222.

  3. Subtract the result of step 2 from 1. Following along, 1 minus 0.00662 would be 0.9993778.

  4. Multiply the result of step 3 by 1,000. This gives you the final figure of $999.38 (1,000 times 0.0003778).


Accrued Interest

Related Articles
  1. Markets

    The Basics Of The T-Bill

    The U.S. government has two primary methods of raising capital. One is by taxing individuals, businesses, trusts and estates; and the other is by issuing fixed-income securities that are backed ...
  2. Managing Wealth

    What to Make of a Zero Percent Yield

    Interest rates hit a new bottom earlier this month when three-month Treasury bills (T-bills) were sold at a zero percent yield for the first time ever.
  3. Managing Wealth

    4 Types Of Money Market Yields

    We give you four equations to help figure out the yields on your investments.
  4. Markets

    How To Read A T-Bill Quote

    If you want buy and sell US Treasury bills, you need to learn to read the quotes.
  5. Trading

    How To Compare Yields On Different Bonds

    Find out how to equalize and compare fixed-income investments with different yield conventions.
  6. Markets

    Calculating Bond Equivalent Yield

    The bond equivalent yield calculates the semi-annual, quarterly or monthly yield on a discount bond or note.
  7. Markets

    The History Of The T-Bill Auction

    Learn how the U.S. found the perfect solution to its debt problems and ended up creating one of the largest markets in the world.
  8. Managing Wealth

    How To Evaluate Bond Performance

    Learn about how investors should evaluate bond performance. See how the maturity of a bond can impact its exposure to interest rate risk.
  9. Markets

    Introduction to Treasury Securities

    Purchasing bonds that are backed by the full faith and credit of the U.S. government can provide steady guaranteed income and peace of mind. Knowing the characteristics of each type of treasury ...
  10. Markets

    How Do I Calculate Yield To Maturity Of A Zero Coupon Bond?

    Yield to maturity is a basic investing concept used by investors to compare bonds of different coupons and times until maturity.
Trading Center