Read a Treasury bill quote from its purchase price

A bill quoted at a 3.6 percent bank discount rate does not earn 3.6 percent of its purchase price over every holding period. The quote is annualized using face value and a 360-day convention. Start with the actual price and maturity payment before interpreting the rate.

TreasuryDirect provides the pricing formula: face value multiplied by one minus the discount rate times days divided by 360. A discounted bill pays face value at maturity; the difference from purchase price is interest.

Recover the payment

Consider an invented $20,000 face-value bill with exactly 120 days between settlement and maturity. Supply a 3.6 percent annual bank discount rate. This is an illustrative quote, not a reported auction. There are no fees, taxes or other payments. The buyer holds to maturity and receives full face value on time.

The price is $20,000 × (1 − 0.036 × 120 ÷ 360), giving $19,760. The discount is $240. Receiving $20,000 after paying $19,760 produces that $240 interest amount; it does not add another annual coupon.

Give the return the right denominator

Divide $240 by $19,760 to obtain the return on the money paid: approximately 1.2146 percent over 120 days. It is a holding-period return, not an annual yield.

To recover the original bank discount quote, instead divide $240 by $20,000 and multiply by 360 divided by 120. The result is 3.6 percent. Changing the denominator and time convention changes the rate label without changing either payment.

Label an annual comparison

A simple 365-day annualization of the purchase-price return is $240 ÷ $19,760 × 365 ÷ 120, approximately 3.6943 percent. This particular comparison scales the period return without compounding. It is not a statement of the official investment-rate formula for every bill maturity.

An effective annual yield would require its own convention. Neither calculation has supplied reinvestment opportunities after this bill matures. Assuming the same short-term return can be earned again is an additional assumption, not a consequence of printing an annualized figure.

The interest-rate and APY comparison explains why an annual yield that includes compounding should not be compounded a second time as though it were a nominal rate.

Keep the holding period explicit

A sale before maturity would replace the $20,000 terminal payment in this record with the actual sale proceeds. The opening discount quote does not guarantee those proceeds. Keep the settlement date, days, purchase amount, terminal receipt and chosen annualization together.

When someone repeats the 3.6 percent figure, ask whether they mean the quote or the return on the cash paid. For a founder's account of decisions behind business figures, read the opening of Infinite Upside.