A Treasury bill calculator needs the right rate and day count

A Treasury bill calculator can answer a simple question: how much cash will a bill purchase require, and how much interest will it produce if held to maturity? The arithmetic is short. Choosing the right inputs is where errors creep in.

Treasury auction results may show a high rate, an investment rate, a price per $100, an issue date, and a maturity date. Those fields are related, but they are not interchangeable. Putting the investment rate into the discount-price formula will not reproduce the official auction price.

For a quick estimate based on an annual yield, use the CD and Treasury Yield Calculator. If an official auction result is available, its price per $100 is the better input for the exact purchase debit.

The four inputs to collect first

Before calculating anything, write down:

1. the face value, sometimes called par value; 2. the discount rate from the auction result; 3. the number of days from issue to maturity; 4. the official price per $100, if it has already been published.

TreasuryDirect's bill page lists regular terms of 4, 6, 8, 13, 17, 26, and 52 weeks. Bills are sold at a discount or at face value. At maturity, Treasury pays the face value. The difference between the amount paid and the maturity payment is the interest.

The minimum TreasuryDirect purchase is $100, and purchases rise in $100 increments. A $10,000 order therefore means $10,000 of face value. It does not mean that exactly $10,000 will leave the linked bank account on the issue date. For a bill sold below face value, the debit will be smaller.

Treasury's discount-price formula

TreasuryDirect gives this formula for estimating a bill's purchase price from its discount rate:

Price = face value × [1 − (discount rate × days ÷ 360)]

Enter the rate as a decimal. A discount rate of 4.20% becomes 0.042. The formula uses a 360-day convention, not 365 days, because the auction discount rate follows a bank-discount basis.

Consider a hypothetical $10,000 bill with 91 days to maturity and a 4.20% discount rate:

Price = $10,000 × [1 − (0.042 × 91 ÷ 360)]

The estimated price is $9,893.83. If the bill is held to maturity and Treasury makes the scheduled payment, it pays $10,000. The difference is $106.17 of interest before federal tax.

These numbers are a math example, not a current Treasury rate or a return forecast. Current terms come from the specific auction result or secondary-market quote.

Price per $100 is the shortest exact calculation

Once Treasury publishes an auction result, it normally provides the price per $100 of face value. That figure avoids rebuilding the price from a rounded rate.

Use:

Purchase debit = price per $100 × face value ÷ 100

If the official price were a hypothetical $98.9383 per $100 and the order were for $10,000 of face value, the calculation would be:

$98.9383 × $10,000 ÷ 100 = $9,893.83

The maturity interest is then:

Interest = face value − purchase debit

Small discrepancies between a hand calculation and the official debit can come from displayed-rate precision, day count, or rounding. The auction result and account transaction control. A homemade spreadsheet does not.

TreasuryDirect's auction guide says that TreasuryDirect bidders submit noncompetitive bids. They choose the face amount and agree to accept the rate set at auction. The exact price becomes known after the auction, and Treasury takes the purchase amount on the issue date.

The discount rate is not the investor's return on cash paid

The discount rate measures the discount against face value and annualizes it using 360 days. An investor actually pays the lower purchase price, so a return measured against cash invested uses a different base.

For the hypothetical example:

Holding-period return = $106.17 ÷ $9,893.83 = about 1.0731%

That is the return for the 91-day holding period before tax, not an annual percentage. Annualizing it with a simple 365-day calculation gives about 4.3040%. Treasury's published investment rate follows its own bill-yield convention, so use the investment rate shown in the auction result rather than treating this shortcut as an official quote.

This is why the high rate and investment rate differ even though they describe the same bill. The high rate helps set the discount price. The investment rate restates the result on a basis intended to be more useful for return comparisons.

Neither should be described as a bank account APY without adjustment. APY assumes a particular compounding convention. A single bill pays at maturity and does not promise that the same rate will be available for reinvestment.

Do not use the term label as the day count

A 13-week label suggests 91 days, but a calculator should use the dates on the actual security. Record the issue date and maturity date from the auction announcement or result, then count the calendar days between them.

The auction date is not the starting date for the interest calculation. Treasury's auction page separates the auction date from the issue date and notes that the two can be days or weeks apart. The issue date is when Treasury delivers the security and collects payment.

This distinction matters when comparing bills with bank products. A person may commit to an auction order on one date, have cash debited on the issue date, and receive face value on the maturity date. The time the cash is invested runs from issue to maturity.

A 52-week bill also should not be forced into a 365-day box. Use the actual dates and the convention attached to the rate being calculated.

A secondary-market bill needs different inputs

The discount-price formula is most useful for a new bill auction when the discount rate and term are known. A bill already trading through a broker has a market price, settlement date, remaining days to maturity, and quoted yield. It may also have a bid-ask spread or brokerage charge.

For a secondary-market purchase, begin with the broker's total price and settlement details. Confirm the CUSIP and maturity date. Then calculate the dollar difference between the total acquisition cost and the face value due at maturity.

Do not take the original auction's discount rate and use it to price the bill today. Market yields may have changed, and part of the term has already passed. The current price reflects the remaining maturity, not the bill's life when issued.

Selling before maturity changes the problem again. The maturity payment is known under the security's terms, but an early sale price depends on the market at that time. A calculator that assumes every bill reaches face value is a hold-to-maturity calculator, not an early-sale estimator.

Taxes belong outside the price formula

TreasuryDirect states that bill interest is subject to federal income tax but not state or local income tax. Tax does not change the auction purchase price. It changes the amount kept after tax.

A rough after-federal-tax estimate is:

After-tax interest = interest × (1 − assumed federal marginal rate)

That shortcut can help compare scenarios, but it is not a tax return calculation. Account type, transaction history, tax rules, and personal circumstances can change the treatment. Use the Tax-Equivalent Yield Calculator to compare hypothetical state and federal assumptions, then confirm the applicable rules from current tax sources.

The state-tax treatment is one reason a Treasury bill and a bank CD with similar headline yields may not produce the same after-tax result. The Treasury bills versus CDs guide also compares liquidity, deposit insurance, maturity, and early-exit mechanics.

Reinvestment is a second calculation

A bill calculator can estimate one purchase through one maturity. It cannot lock the yield on the bill that comes next.

Suppose a 13-week bill matures and the proceeds are reinvested. The new bill will be priced at a later auction. Repeating today's return four times assumes that future auctions produce the same rate, which Treasury does not promise.

Keep the first calculation narrow:

  • cash required on the issue date;
  • face value paid at maturity;
  • interest earned over that bill's actual term;
  • estimated tax effect, if included.

Build any reinvestment scenario separately, with a stated rate assumption for each later term. That makes it obvious which returns come from an official result and which are guesses about future auctions.

A spreadsheet setup that is easy to audit

A useful worksheet needs only a few columns:

| Field | Entry or formula | |---|---| | Face value | Order amount in $100 increments | | Issue date | From the auction announcement or result | | Maturity date | From the same security record | | Days | Maturity date minus issue date | | Discount rate | High rate for the price formula, entered as a decimal | | Estimated price | Face value × [1 − (discount rate × days ÷ 360)] | | Official price | Published price per $100 × face value ÷ 100 | | Interest | Face value minus official purchase price | | Holding-period return | Interest ÷ official purchase price |

Keep the estimated and official prices in separate cells. If they differ, do not overwrite the official figure to make the sheet look tidy. Check whether the entered rate was rounded, whether the correct dates were used, and whether the formula accidentally used the investment rate.

Also label every rate. A cell named simply "yield" invites confusion six months later.

What the calculator can and cannot tell you

It can calculate the purchase debit and maturity interest for a specified bill. It can also put the bill's dollar return next to a CD estimate or another short-term cash option.

It cannot tell you whether the money will be needed before maturity, what rate will be available later, what an early sale would produce, or how a tax rule applies to a particular return. Those questions need their own inputs.

Start with the security's official dates and price. Use the discount formula as a check, not as a replacement for the auction result. Browse the Economy section for more guides on Treasury auctions, inflation, interest rates, and cash planning.

Educational only. This article provides general information and hypothetical calculations. It is not personalized financial, investment, tax, legal, or accounting advice, and it does not recommend buying or selling any security.

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