T-bill discount yield calculator
A Treasury bill's discount rate, price, investment rate and money market yield all describe the same bill. Enter the rate or the price and the term to see all of them, worked through step by step.
Discount yield
4.000%
bank discount basis, 360-day year
Investment rate
4.139%
bond-equivalent (coupon-equivalent) yield
Money market yield
4.083%
simple interest, actual/360
| Price per 100 | 97.977778 |
|---|---|
| Purchase price for $1,000 face value | $979.78 |
| Discount the interest you earn at maturity | $20.22 |
- Price
100 × (1 − 0.040000 × 182 ÷ 360) = 97.977778 - Investment rate
(100 − 97.977778) ÷ 97.977778 × 365 ÷ 182 → 4.139% - Money market
(100 − 97.977778) ÷ 97.977778 × 360 ÷ 182 = 4.083%
Three yields for one bill
Treasury bills pay no coupon. They sell at a discount and repay face value at maturity, and the difference is the interest. The same price can be quoted three ways (r = days to maturity):
- Discount yield: the discount as a share of face value over a 360-day year, the basis bills are auctioned on. Price per 100 = 100 × (1 − d × r ÷ 360).
- Investment rate: the coupon-equivalent yield Treasury publishes with each auction, measured on the price paid over a 365- or 366-day year so it compares with note and bond yields. Bills longer than half a year are solved as a quadratic.
- Money market yield: simple interest on the price over an actual/360 year, the basis of Treasury's floating rate note index.
The year after the issue date counts as 366 days when it contains 29 February; with dates the calculator checks this for you.
TreasuryDirect's example: a $1,000 26-week (182-day) bill at a 0.145% discount rate costs 1,000 × (1 − 0.00145 × 182 ÷ 360) = $999.27, a discount of $0.73. Load it with the example button.
Sources
- U.S. Treasury, 31 CFR Part 356, Appendix B, section VI (bill price, discount rate and investment rate formulas, with worked examples this calculator reproduces) and section I.C (the money market yield on an actual/360 basis).
- TreasuryDirect, Understanding pricing and interest rates (the $999.27 example) and Treasury bills (terms of 4, 6, 8, 13, 17, 26 and 52 weeks).
Questions
Why is the investment rate higher than the discount rate?
The discount rate divides the interest by face value and uses a 360-day year. The investment rate divides it by the lower price you actually pay and uses a 365-day year, and both push it up.
Which yield compares with a Treasury note's yield?
The investment rate, which is why Treasury also calls it the coupon-equivalent yield. The money market yield lines up with rates quoted on an actual/360 basis.
How are prices rounded?
Treasury rounds the price per $100 to six decimal places, and so does this calculator before working out the other yields. The dollar cost for your face value is rounded to the cent.