# U.S. Treasury Bill Math

Money market securities mature in less than a year and pay simple interest (as opposed to compound interest). Treasury bills are money market instruments that pay simple interest, but are quoted (sold) based on a discount rate. Securities that use a discount rate can be thought of as paying the interest upfront, as opposed to paying interest at maturity. Paying interest upfront has an advantage over paying at maturity due to the time value of money which I touched on in the post of the same name. Don’t think the Treasury is doing you any favors however, by paying upfront interest. The discount rate is lower than the money market rate and so is the interest paid. Below is an example of a 241 day bill, quoted at a 5.0% discount rate. The bottom boxes show that the dollar amount paid for $1 million in face value is $966,527.78, which means the interest earned upfront is $33,472.22. The investor gets back the $1 million face value at maturity.

Converting the discount rate to a money market rate (all the formulas are further down this post) we get a 5.17316% money market equivalent rate, which would pay $34,631.41 in interest if paid at maturity. The money market rates of return are both 5.17316%.

Money Market Rate of Return = (ending value / starting value)*360/241

Below are various math formulas to equate discount rates with money market rates. The yellow cells are input cells and the red letters are named values.

In addition are the formulas for calculating the Bond Equivalent Yield (BEY). There are two formulas. The first is the BEY for bills less than or equal to 182 days to maturity. The second formula is for bills over 182 days to maturity. Why two formulas? The first simply converts the day count from actual/360 to actual/365, which Treasury bonds use. The second formula is more complicated due to the bond being compared will have a single coupon payment, which requires reinvesting (compound interest).

Note that the yellow cell has a drop down box to enter either 365 or 366, depending upon if you are in a leap year.

Download spreadsheet “T-Bills.xlsx“

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