What Is a U.S. Treasury Bill?
A bill has no periodic coupon: the difference between its purchase price and face value is the gross amount earned if held to maturity. Treasury sells bills at a discount or at par. An early sale, taxes, fees, and inflation can change the investment outcome; none is modeled here.
Maturities and Actual Days
TreasuryDirect lists 4, 6, 8, 13, 17, 26, and 52-week bills. The first six are auctioned weekly; 52-week bills every four weeks. Cash Management Bills have variable terms and no regular schedule. Check the auction announcement for the security you are considering.
The calculator presets multiply weeks by seven. When settlement or maturity differs from a standard term, enter the dates or actual remaining days. Date mode counts calendar days between the supplied dates; it does not adjust weekends, holidays, settlement lags, or auction conventions. Supported maturities are 1–366 whole days.
Price from a Bank Discount Rate
With face value F, annual discount rate d as a decimal, and D days, the calculator uses P = F × (1 − d × D / 360). The entered rate is a discount quote, not an effective annual yield. Zero discount gives par value. Inputs that produce a nonpositive price are rejected.
Hypothetical example: F = $10,000, d = 5%, and D = 182 gives P = $9,747.2222 before rounding, and a $252.7778 gross difference at maturity. Displayed cents are rounded; this is not a current auction quote or a guaranteed executable price.
Four Yield Conventions
Let h = (F − P) / P be the holding-period return. The formulas below produce decimal rates; the results panel multiplies them by 100 to show percentages. The model accepts prices at or below par only.
- Bank Discount Yield: (F − P) / F × 360 / D. This uses face value rather than the cash invested.
- Money Market Yield: h × 360 / D. This is a simple annualization on the purchase-price base.
- Bond Equivalent Yield estimate: h × 365 / D through 182 days. Above 182 days, set a = D / 365 and use 2h / (a + √(a² + (2a − 1)h)). This is the positive coupon-equivalent root under this model’s fixed 365-day basis.
- Effective Annual Yield: (1 + h)^(365 / D) − 1. It assumes the same holding-period return can be reinvested across a year; future reinvestment rates are unknown.
The model uses 365 even in leap years and does not reproduce every official auction rounding rule. Use Treasury’s published investment rate and settlement amount when reconciling an actual purchase. Different annualization conventions answer different questions; no single displayed yield establishes the best investment.
Use the Results
- Enter a known purchase price in Yield mode, or a discount quote in Price mode.
- Enter actual days or settlement and maturity dates. A preset is only a shortcut.
- Calculate, then compare both gross dollars and the selected annualization convention.
- Changing an input clears the prior result. Invalid inputs show a reason instead of retaining an apparently current answer.
This is a manual-input educational calculator. It does not fetch rates, recommend a purchase, submit bids, calculate tax, or save a portfolio. The calculated return assumes holding to maturity before costs.