How to use the t-bill yield calculator
- Choose what you know: the price paid or the discount rate.
- Enter the face value, the amount paid at maturity, and the days to maturity, from 1 to 182.
- Enter the price or the discount rate, depending on your choice.
- Read the price, the discount rate, the money market yield, the bond equivalent yield and the effective annual yield.
Formula
discount rate = (face - price) / face x 360 / days
price = face x (1 - discount rate x days / 360)
money market yield = (face - price) / price x 360 / days
bond equivalent yield = (face - price) / price x 365 / days
effective annual yield = (face / price)^(365 / days) - 1
The discount rate measures the discount against the face value and uses a 360 day year. The investment yields measure the same gain against the price paid, which is the money actually invested.
A 91 day bill priced at $9,876.50
A bill with a face value of $10,000 matures in 91 days and costs $9,876.50, a discount of $123.50. The discount rate is 123.50 / 10,000 x 360 / 91 = 4.8857 percent. The money market yield is 123.50 / 9,876.50 x 360 / 91 = 4.9468 percent, and the bond equivalent yield on a 365 day year is 5.0155 percent.
Compounding the gain over a year gives an effective annual yield of 5.1107 percent. Going the other way, a 182 day bill quoted at a 4.5 percent discount rate costs $10,000 x (1 - 0.045 x 182 / 360) = $9,772.50.
Why one bill has several yields
Short term bills are sold at a discount to face value, and different markets quote the return in different ways. The discount rate is a quoting convention and understates the return, because it divides by the larger face value and a 360 day year. The investment yields divide by the price you paid, which is how most people think about a return.
To compare a bill with a bond or a savings account, use the bond equivalent yield or the effective annual yield, which put everything on a 365 day year.
Limits of this page
The page uses a simple formula for terms up to 182 days. Longer bills use a different formula in practice, so the page stops there. It does not look up prices or auction results, and it ignores taxes and fees. For bonds that pay coupons, use the Bond Yield Calculator. To convert a nominal rate to an effective one, use the APY and APR Calculator.
Assumptions and limits
- The bill pays the face value at maturity and nothing before.
- The discount rate uses 360 days a year. The bond equivalent and effective yields use 365.
- Settlement and maturity are counted as a whole number of days.
- Taxes, fees and reinvestment of the gain are not modeled, except the compounding in the effective annual yield.
- The prices and rates shown when the page opens are examples, not quotes.
Frequently asked questions
Why is the bond equivalent yield higher than the discount rate?
The discount rate divides the gain by the face value and uses 360 days. The bond equivalent yield divides by the smaller price actually paid and uses 365 days, so the same gain gives a higher number.
What does the effective annual yield assume?
It assumes you can roll the money over into the same return for a full year. If rates change, the real result will differ.
Why does the page stop at 182 days?
Beyond about six months the simple bond equivalent formula no longer matches how longer bills are quoted. The page covers the range where the simple formula holds.
Can I enter a price above the face value?
No. A discount security sells below face value. The page asks for a price below the face value so the gain is positive.