A T-bill’s discount rate understates what it pays. This calculator converts between the discount rate, the price per $100 and the investment rate (bond-equivalent yield) with Treasury’s own formulas, and adds the money-market yield. At the 3-month Treasury yield of 4.260% on 2026-10-13 (investment basis, FRED DGS3MO), a 13-week bill of 91 days costs 98.949079 per $100: $9,894.91 for $10,000 of face value, which pays $105.09 more at maturity. Its discount rate is 4.157% and its money-market yield 4.202%.
Inputs
Result91 days, 365-day year
Price per $100
98.949079
Discount rate
4.157%
Investment rate (bond-equivalent)
4.260%
Money-market yield
4.202%
You pay
$9,894.91
Interest at maturity
$105.09
Maturity date
2027-01-12
Investment rate from the simple formula (183 days or less). Price rounded to six decimals and rates to three, as Treasury publishes them.
Formulas
Treasury’s rules for bills (31 CFR Part 356, Appendix B). P is the price per $100 of face value; d, i and m are the discount rate, the investment rate and the money-market yield, as decimals; t is the number of days to maturity; y is 365, or 366 when the year after the issue date includes 29 February.
Price from the discount rate
P = 100 × (1 − d × t / 360)
Discount rate from the price
d = (100 − P) / 100 × 360 / t
Investment rate, 183 days or less
i = (100 − P) / P × y / t
Investment rate, over 183 days (solved for i)
P × [1 + (t − y/2) × i / y] × (1 + i/2) = 100
Money-market yield
m = (100 − P) / P × 360 / t
Treasury rounds the price to six decimals and states rates to three; the calculator does the same, so it reproduces published auction results. The longer formula applies from 184 days: that cutoff matches the published results of all 3,169 bill auctions from 2015 to 2026 that we checked.
Frequently Asked Questions
What is the difference between a T-bill’s discount rate and its investment rate?
The discount rate is the discount from face value, annualised on a 360-day year and divided by face value, not by the price paid. The investment rate, also called the bond-equivalent or coupon-equivalent yield, divides by the price and uses a 365-day year (366 in a leap year), so it is always the higher of the two and the one to compare with a note or bond yield. For the bill above, a discount rate of 4.157% is an investment rate of 4.260%.
How do I calculate a T-bill’s price from the discount rate?
Price per $100 = 100 × (1 − d × t / 360), with d the discount rate as a decimal and t the days to maturity. For 91 days at 4.157% that is 98.949079, so $10,000 of face value costs $9,894.91. Treasury rounds the price to six decimals before it computes the other rates.
Why does a 52-week bill use a different formula?
The investment rate puts a bill on the same footing as a note that pays interest every six months. For a bill longer than half a year, Treasury assumes the first half-year’s interest is reinvested at the same rate, which makes the price equation quadratic in i. Up to 183 days the simple formula applies, so 4- to 26-week bills use it and 52-week bills (364 days) do not.
What is a T-bill’s money-market yield?
Simple interest on the price paid, on a 360-day year: (100 − P) / P × 360 / t. It is higher than the discount rate and lower than the investment rate. Certificates of deposit and other money-market instruments are often quoted this way, so it is the figure to compare with them.