Treasury Bill (T-Bill) Calculator
This calculator supports the three common T‑Bill workflows: start from the quoted bank discount rate, from an observed market purchase price, or from a bond‑equivalent (investment) yield. Results include the purchase price, profit at maturity, the bank discount yield (quoted on a 360‑day basis) and the bond‑equivalent yield (annualized on actual/365).
Defaults follow market conventions used for U.S. Treasury bills: bank discount quotes use a 360‑day base; bond‑equivalent yields are annualized on 365 days. Use the method selector to switch workflows and enter values as decimals for rates (for example, 0.05 = 5%).
Compute purchase price and equivalent yields given the bank-discount convention (d) used for T‑bills.
Inputs
Advanced inputs
Inputs for discount-rate mode
Inputs for price mode
Inputs for yield mode
Results
Purchase price
$987.36
Profit at maturity
$12.64
Bond‑equivalent (investment) yield
5.13%
Bank discount yield (quoted)
5.00%
| Output | Value | Unit |
|---|---|---|
| Purchase price | $987.36 | currency |
| Profit at maturity | $12.64 | currency |
| Bond‑equivalent (investment) yield | 5.13% | % |
| Bank discount yield (quoted) | 5.00% | % |
Visualization
Methodology
Bank discount convention: T‑Bill discount yields (d) are quoted relative to face value using a 360‑day year. Price is P = F × (1 − d × (days/360)).
Bond‑equivalent (investment) yield converts the realized return to an annualized yield on an investment basis: y_BE = ((F − P) / P) × (365 / days).
When computing from a given BEY, price is computed as P = F / (1 + y_BE × (days/365)). All methods compute profit as F − P.
Worked examples
Example 1 — From discount: Face = 1000, d = 0.05, days = 91 → P = 1000 × (1 − 0.05 × 91/360) = 987.36 (approx), profit = 12.64, BEY ≈ (12.64 / 987.36) × (365/91) ≈ 0.0527 (5.27%).
Example 2 — From price: Face = 1000, P = 975, days = 182 → d = ((1000−975)/1000) × (360/182) ≈ 0.0495 (4.95%), BEY ≈ ((25)/975) × (365/182) ≈ 0.0512 (5.12%).
Example 3 — From BEY: Face = 1000, y_BE = 0.06, days = 28 → P = 1000 / (1 + 0.06 × 28/365) ≈ 995.42, profit ≈ 4.58, discount yield ≈ (4.58/1000) × (360/28) ≈ 0.0589 (5.89%).
Further resources
Expert Q&A
Why are there different yields (discount yield vs bond‑equivalent yield)?
Bank discount yield is a market quoting convention based on face value and a 360‑day base. Bond‑equivalent yield reflects the investor's actual return on the cash invested and is annualized on an actual/365 basis. They are different because they use different denominators and day‑count conventions.
Which day‑count basis is used?
This tool uses the common market conventions for U.S. Treasury bills: bank discount calculations use a 360‑day base; bond‑equivalent yields use a 365‑day base for annualization.
How precise are the results?
Results are computed using standard arithmetic expressions and rounded for display. Small rounding differences may occur versus broker systems that use extended precision or different intraday conventions. See the accuracy and testing notes in citations.
Can I change the face value or days to maturity?
Yes. Face value (par) and days to maturity are editable. Use the method selector to provide the appropriate input for the chosen workflow.
Sources & citations
- U.S. Treasury — Daily Treasury Bill Rates and conventions — https://home.treasury.gov/resource-center/data-chart-center/interest-rates
- NIST — Guidelines for numerical software quality and validation — https://www.nist.gov
- ISO — Quality management standards (ISO 9001) — https://www.iso.org/iso-9001-quality-management.html
- IEEE — Standards for software verification and validation — https://www.ieee.org
- OSHA — Guidance on recordkeeping and validation of test procedures — https://www.osha.gov