Treasury Bill Yield Calculator
Treasury bill price, discount, and investment rate from discount yield and days.
What it does
Treasury bills pay no coupons: you buy below face and collect face at maturity, and the discount is the interest. Two yields describe that deal, and mixing them up misprices every comparison.
The tool above takes face value, discount rate, and days. It returns the price, the dollar discount, and the investment (coupon-equivalent) rate.
The default $1,000 26-week bill at 4.5% costs $977.25, earns $22.75, and annualizes to 4.67%. The TreasuryDirect 0.145% example reprices to $999.27 with a 0.15% investment rate.
Formulas follow TreasuryDirect pricing pages with 31 CFR 356 Appendix B behind them. Both pin the 360-day discount basis against the 365-day investment basis used here.
How to use
- Enter the face (par) value.
- Enter the discount rate in percent.
- Enter actual days to maturity.
- Pick 365 or 366 for the year basis.
- Read price first, then discount.
- Compare with the investment rate.
Formula
- face
- Amount paid at maturity.
- rate
- Bank discount rate as a percent.
- days
- Actual days from settlement to maturity.
- year-days
- 365, or 366 across a Feb 29.
Discount yield uses the face base with 360 days; investment rate uses the price paid with 365 days, or 366 when the year from issue holds Feb 29. Rates display to 2 decimals here; auctions round per Treasury procedure.
Worked example
Example: 26-week bill at 4.5%
Defaults: $1,000 face, 4.5% discount rate, 182 days, 365-day year.
- Discount factor: 0.045 x 182 / 360 = 0.02275.
- Price: 1,000 x (1 - 0.02275) = $977.25.
- Discount: 1,000 - 977.25 = $22.75.
- Holding return: 22.75 / 977.25 = 0.0232764.
- Annualize: x 365 / 182 = x 2.0054945.
- Investment rate: 0.0466806 = 4.67%.
- Tool shows $977.25, $22.75, 4.67 %.
Reference table
| Yield | Divides by | Year |
|---|---|---|
| Discount yield | Face (par) | 360 days |
| Investment rate | Price paid | 365 days |
| Leap investment rate | Price paid | 366 days |
| Holding return | Price paid | Actual days |
Limits
- Bills past one half year need the Treasury quadratic.
- Auction rounding differs slightly from display.
- Secondary market prices add accrued timing.
- Tax treatment sits outside the math.
Common mistakes
- Comparing discount yields with coupon yields.
- Using 365 in the discount leg.
- Forgetting Feb 29 leap basis.
- Annualizing 52-week bills with the short formula.
- Reading price per 100 as price per 1,000.
Try it yourself
Quick checks. Answers sit tucked under each question.
$100 bill, 4.5%, 91 days?
Price 100 x (1 - 0.011375) = $98.86, discount $1.14, rate 4.61%.
Default bill on a 366-day basis?
Same $977.25 price, investment rate 4.68% on the 366 basis.
TreasuryDirect 0.145% example?
Price $999.27, discount $0.73, investment rate 0.15%.
Questions
Why is the investment rate higher?
The discount rate divides by face on a 360-day bank basis, so it understates true return. Compare bills with the investment rate.
How is auction price set?
Yes: price = face x (1 - rate x days / 360). The TreasuryDirect 0.145% example gives $999.27 on $1,000.
When does the year count 366 days?
Use 366 when the year from issue date holds Feb 29, else 365, per 31 CFR 356.
What about 52-week bills?
Past one half year the Treasury uses a semiannual coupon-equivalent formula, not the simple annualization here.
Are T-bills zero coupon?
Yes. Bills sell below face and pay face at maturity; the discount is the interest.
How are T-bills taxed?
Federal tax applies to the discount; most states exempt it. See a tax pro for your case.