Bank Bill Pricing Formula

Q: A 90-day bank bill with face value A$1 million and yield 5.00% is priced at

A987,808.P = 1{,}000{,}000/(1 + 0.05 \times 90/365) = 1{,}000{,}000/1.01233 = A987,808. The other answers reflect compound interest, naive subtraction, or adding instead of discounting interest.

Q: If the yield on a 60-day bank bill rises from 4.50% to 4.75%, the price will

Fall, because the discount factor 1 + y × d/365 grows. Price equals face value divided by 1 + y × d/365. As y rises, the denominator rises and the price falls. Bond prices and yields always move inversely under any time-value-of-money formula.

Australian bank-accepted bills are priced by simple-interest discounting of face value, $P = FV/(1 + y \times d/365)$ . The convention is set by the Australian Financial Markets Association (AFMA) and follows ACT/365. $FV$ is face value, $y$ is the annualised yield, and $d$ is the number of calendar days to maturity. The same formula prices negotiable certificates of deposit and Treasury Notes in the AUD market.

Try it yourself

Bond price vs yield

A bond's price is the present value of its coupons plus face, discounted at the market yield. Move the yield and watch price trace the downward-sloping, convex curve — price moves inversely to yield.

Price 100.00Current yield 5.00%Coupon income 5.00/yr

parcoupon = yield, price = face

Coupon rate5.0%

Yield to maturity5.0%

Years to maturity5 yr

Coupon frequency

Face value fixed at 100, so price reads as a percent of face.

Why it matters

The formula is the present value of a single future cash flow under simple interest. A 90-day bill paying A$100,000 at maturity, with money costing 5% a year, must be worth less than A$100,000 today. Dividing by 1 + 0.05 × 90/365 recovers the cash you would lend now to grow to A$100,000 in 90 days. The longer the time and the higher the yield, the bigger the discount and the lower the price. Bank bill yields move with BBSW and the RBA cash rate.

Before you read on — recall

A 90-day bank bill with face value A$1 million and yield 5.00% is priced at

Formulas

Bank bill price

P = \frac{FV}{1 + y \times d/365}

Implied yield from price

y = \left(\frac{FV}{P} - 1\right) \times \frac{365}{d}

Bank bill futures quoted price

Q = 100 - y \times 100

ASX 90-day bank bill futures use the 100-minus-yield quotation. A yield of 4.50% corresponds to a futures price of

Q = 95.50

Worked examples

Scenario

Face value A$500,000, 60 days to maturity, market yield $y = 4.80\%$ .

Solution

$P = 500{,}000/(1 + 0.048 \times 60/365) = 500{,}000/1.007890 =$ A$496,085.97. Interest earned at maturity $=$ A$3,914.03, equivalent to 4.80% per annum simple.

Scenario

Solve for the implied yield on a bank bill purchased at A$987,808 with face value A$1,000,000 and 90 days to maturity.

Solution

$y = (1{,}000{,}000/987{,}808 - 1) \times 365/90 = 0.012340 \times 4.0556 = 0.05003 = 5.00\%$ . Yields are quoted to two basis points in interbank dealing.

Scenario

An ASX 90-day bank bill futures contract is quoted at $Q = 95.50$ . Convert to yield and compute the contract value (notional A$1,000,000, 90-day reference period).

Solution

Implied yield $y = 100 - 95.50 = 4.50\%$ . Contract value $= 1{,}000{,}000/(1 + 0.045 \times 90/365) =$ A$989,026. A one-basis-point move (one tick) changes this discounted contract value by approximately A$24.12 at this yield. The crude linear figure $\,1{,}000{,}000 \times 90/365 \times 0.0001 \approx$ A$24.66 ignores the discount denominator and slightly overstates the true tick value.

Common mistakes

✗Bank bill pricing uses compound interest. AUD bank bills are simple interest discount instruments, not compounded. Using $(1+y)^{d/365}$ in place of 1 + y × d/365 gives the wrong price by a few cents on a 90-day bill and meaningful amounts on longer paper.
✗Price and yield move in the same direction. They are inverses. The denominator 1 + y × d/365 rises with yield, so price falls. A 25 basis-point rate rise drops a 90-day A$1 million bill price by roughly A$615.
✗The 360-day year applies in Australia. AUD money market uses ACT/365. The 360-day convention is the US T-bill discount basis and euro money market standard. Plugging US conventions into AUD bill formulas introduces a 1.4% error in computed price.

Revision bullets

• $P = FV/(1 + y \times d/365)$ for AUD bills
•Simple interest ACT/365, AFMA convention
•Price and yield are inversely related
• $y = (FV/P - 1) \times 365/d$ inverts the formula
•ASX bank bill futures quoted as 100 - $y$
•Tick value of 1 bp on 90-day A$1m bill $\approx$ A$24.12 (discount basis)

Quick check

A 90-day bank bill with face value A$1 million and yield 5.00% is priced at

If the yield on a 60-day bank bill rises from 4.50% to 4.75%, the price will

Connected topics

100 - Y T-bills

More in Debt & Yield Curves

Money Mkt Comm. Paper CDs MMF Yield Curves Zero Rates Forward Rates Bond Price

In learning paths

Fixed Income & Rates Path

Sources

AFMA Bank Bill Convention
Australian Financial Markets Association. AFMA Conventions for Negotiable and Transferable Instruments. AFMA, accessed 2026.
Official source for the simple interest ACT/365 formula used for AUD bank bills, NCDs, and Treasury Notes.
ASX 90 Day Bank Bill Futures
Australian Securities Exchange. 90 Day Bank Accepted Bill Futures Contract Specifications. ASX, accessed 2026.
Contract spec providing the 100-minus-yield quotation, A$1 million notional, and tick value formula.
Hull (2022), §6
Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
Chapter 6 covers short-term interest rate futures and the discount-basis pricing used for AUD and USD bills.
RBA Bulletin (Sept 2018)
Reserve Bank of Australia. Interest Rate Benchmarks for the Australian Dollar. RBA Bulletin, September 2018.
BBSW methodology and the relationship between bank bill yields and the benchmark.
Fabozzi (2021), Ch. 12
Fabozzi, Frank J. Bond Markets, Analysis, and Strategies. 10th ed. MIT Press, 2021. ISBN 978-0-262-04627-3.
Money market chapter covering discount instrument pricing across jurisdictions and conventions.

How to cite this page

Dr. Phil's Quant Lab. (2026). Bank Bill Pricing Formula. Derivatives Atlas. https://phucnguyenvan.com/concept/bank-bill-pricing