Treasury Bill Discount Price CalculatorFree online financial calculator — instant results, no sign-up
Price a Treasury bill from its bank discount yield using a 360-day convention.
Estimates only, based on the inputs and assumptions shown. This is not financial, investment, tax, or legal advice. Prices, rates and local rules may change; crypto scenarios do not predict returns. Confirm important decisions with a qualified professional.
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About the Treasury Bill Discount Price Calculator
The Treasury Bill Discount Price Calculator converts a bank discount yield into a Treasury bill purchase price using a 360-day year. Enter the bill’s face value, quoted bank discount yield, and days to maturity to calculate its price, discount earned, and simple annualized investment yield on a 365-day basis.
- Face value ($)
- The amount paid back when the Treasury bill matures, in dollars; the default is $10,000.
- Bank discount yield (%)
- The annualized discount quoted as a percentage of face value on a 360-day basis; the default is 4.5%.
- Days to maturity (days)
- The number of actual days from settlement to maturity, in days; the default is 182.
Formula and method
d = q / 100; D = F × d × (t / 360); P = F − D = F × [1 − d × (t / 360)]; Y = (D / P) × (365 / t) × 100%. With the default inputs: D = 10000 × 0.045 × (182 / 360) = $227.50; P = 10000 − 227.50 = $9,772.50; Y = (227.50 / 9772.50) × (365 / 182) × 100% ≈ 4.67%.
- FFace value in dollars, payable at maturity.
- qBank discount yield entered as a percentage, such as 4.5.
- dBank discount yield expressed as a decimal: q / 100.
- tActual days remaining from settlement to maturity.
- DDollar discount, equal to face value minus purchase price.
- PCalculated purchase price in dollars.
- YSimple annualized investment yield expressed as a percentage on a 365-day basis.
Convert the quoted percentage yield to a decimal, then multiply it by face value and days to maturity divided by 360 to find the dollar discount. Subtract that discount from face value to obtain the purchase price. Divide the discount by the purchase price and multiply by 365 divided by days to maturity to annualize the investment return without compounding. Keep full precision during calculation, then display dollar amounts and percentage yield to two decimal places.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Face value10000 $
- Bank discount yield4.5 %
- Days to maturity182 days
Results
- Purchase price$9,772.50
- Discount earned$227.50
- Simple investment yield on 365-day basis4.67%
How to use the Treasury Bill Discount Price Calculator
- 1Enter the Treasury bill’s face value in dollars; use 10000 for the default example.
- 2Enter the bank discount yield as a percentage; use 4.5, not 0.045, for the default example.
- 3Enter the actual days remaining to maturity; use 182 for the default example.
- 4Calculate the results and review the purchase price of $9,772.50 and discount earned of $227.50.
- 5Review the simple investment yield on a 365-day basis of 4.67%, which measures annualized return relative to the purchase price.
Reading your result
Purchase price is the amount implied by the quoted bank discount yield: $9,772.50 with the default inputs. Discount earned is the difference between face value and purchase price: $227.50 received as the gain if the bill is held to maturity and repaid at face value, before costs and taxes. Simple investment yield on a 365-day basis is that gain divided by the amount invested and annualized without compounding: 4.67%. It is not the return earned over the 182-day holding period itself.
Limitations
This calculator assumes a non-coupon Treasury bill purchased at the calculated price and held to maturity. The quoted yield must be a bank discount yield, not an investment yield or effective annual yield. Pricing uses a fixed 360-day denominator, while the simple investment yield uses 365 even in a leap year. Results exclude taxes, fees, bid–ask spreads, reinvestment, and price changes before maturity, and may differ from executable market quotes or settlement rounding. Face value and days to maturity must be positive, and the inputs must imply a positive purchase price for the investment-yield calculation to be meaningful.
Common questions
Why is the default investment yield 4.67% when the bank discount yield is 4.5%?+
The 4.5% bank discount yield uses the $10,000 face value and a 360-day year. The 4.67% simple investment yield uses the lower $9,772.50 purchase price and a 365-day year. These different denominators make the investment yield higher for the default positive discount.
Does the $227.50 discount arrive as a separate interest payment?+
No. In the default example, you pay $9,772.50 and receive $10,000 at maturity. The $227.50 difference is the discount earned rather than a separate coupon payment.
Should I enter 182 actual days or adjust the term to a 360-day calendar?+
Enter 182 actual days for the default example. The 360-day convention applies only to the annual denominator in the discount-price formula; it does not replace the actual day count with twelve 30-day months.
Can I enter a Treasury bill’s investment yield in the bank discount yield field?+
No. This field requires a yield quoted on face value using the bank discount convention. Entering an investment yield directly would produce the wrong price because investment yields use the purchase price as their return base.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.