Treasury Bill Yield Calculator (Discount Rate to Price and Yield)
Price of a discount security such as a Treasury bill from its quoted discount rate, with the bond-equivalent, money-market and effective annual yields.
Results
What this tool does
Bills are quoted on a bank discount basis: the discount rate is applied to the face value over a 360-day year, so it understates what an investor really earns, because the profit is measured against the lower price paid rather than the face value. The bond-equivalent yield restates the return against the price on a 365-day year so it can be compared with coupon bonds; the money-market yield uses 360 days to compare with deposits and CDs. For longer bills the compounded effective yield is a little higher still. Day-count conventions differ between markets, so check the one that applies to your bill.
Formula
price = face × (1 − d × t ÷ 360) · BEY = (F − P) ÷ P × 365 ÷ t · MMY = (F − P) ÷ P × 360 ÷ t
Variables
| Symbol | Meaning | Unit |
|---|---|---|
fv | Face (par) value of the bond | — |
d | Quoted discount rate (bank discount basis) | % |
t | Days to maturity | d |
P | Price to pay | — |
DS | Discount from face value | — |
BEY | Bond-equivalent yield (365-day year) | % |
MMY | Money-market yield (360-day year) | % |
EAY | Effective annual yield (compounded) | % |
Worked example
- Face (par) value of the bond1000
- Quoted discount rate (bank discount basis)5 %
- Days to maturity91 d
- Price to pay987.3611
- Discount from face value12.6389
- Bond-equivalent yield (365-day year)5.1343 %
- Money-market yield (360-day year)5.0640 %
- Effective annual yield (compounded)5.2341 %
Limitations
- This is an informational calculator, not personalised financial advice. Rates, fees, taxes and contract conditions vary between institutions and countries.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.