Treasury bill discount rate vs. investment rate: why they differ

Treasury’s example pairs a $1,000 face-value bill with a 0.145% discount rate, a published $999.27 purchase price and $0.73 interest after 182 days, or 26 weeks. Those cash flows come first: discount rate and investment yield describe the bill using different percentage bases and year lengths.12

Start with the price paid and the dollars returned

Face value is the amount repaid at maturity. For a bill bought at a discount, the discount is the difference between face value and purchase price. Treasury calls that difference interest: paying the published $999.27 and receiving $1,000 at maturity produces its published $0.73 interest.1

Treasury’s published price formula is: Price = Face value (1 – (discount rate x time)/360).1

Its worked substitution is: Price = 1000 (1 – (.00145 x 182)/360) = $999.27.1

Here, 1000 is face value; .00145 is the quoted 0.145% expressed as a decimal; and 182 is the number of days to maturity. The 360 represents the discount quotation’s year basis. Treasury displays the resulting purchase price to cents.12

The denominator and year basis change the quoted return

The denominator is the amount used as the percentage base. Bank discount uses face value; investment yield uses purchase price. For the published example, the bank-discount convention relates the gain to the $1,000 due at maturity. The investment-yield convention instead relates it to the $999.27 actually paid. A given gain is a larger percentage of a smaller base. That difference exists before considering the calendar: the bank-discount quotation also uses a 360-day year, while Treasury describes investment yield on a 365- or 366-day basis. Changing the base and changing the year length are separate steps in expressing the return.21

Investment yield is also called coupon equivalent or bond equivalent. Treasury says coupon equivalence permits comparison with a nominal coupon security paying semiannual interest—interest twice a year—and maturing on the same date. That comparison changes how the return is expressed; it does not change the bill’s payments.21

Separate dollars earned from a yearly quotation

Follow the same published cash flows from the investor’s side. The investor pays $999.27, receives $1,000 at maturity and earns the published $0.73 over 182 days. Relating that $0.73 gain to the $999.27 paid gives the return for this holding period. The denominator is the money committed to obtain the gain, and the period is 182 days. The holding period is shorter than a year. To express a holding-period return as a simple annual yield, scale it by the applicable number of days in a year relative to the days in the holding period. The percentage is being put on a yearly scale; the bill’s dollar payment and maturity date remain the same. No extra return percentage is needed to see why this differs from a quotation based on $1,000 and a 360-day year.132

Treasury’s glossary defines investment yield as annualized simple interest without compounding. Compounding adds earned interest to principal so that interest itself earns interest. Simple annualization excludes that process: expressing a shorter holding on a yearly scale does not make the bill pay interest for a full year.3

Check whether the quotation comes from an auction or trading

Treasury’s example describes an auction, where competitive bids establish the discount rate and price. The secondary market trades previously issued securities. Treasury’s daily bill rates are secondary-market quotations for the most recently auctioned bills at each maturity, collected by the New York Fed around 3:30 PM each business day.132

The educational example has no identified auction date. Retrieval on September 11, 2026 does not date it or establish a currently available yield. Its applicable 365- or 366-day investment-yield basis is also unspecified.123

Early sales and reinvestment require their own terms

Bills can be sold at par, meaning face value, or at a discount. Face-value repayment applies at maturity. Investors may sell earlier, but that secondary-market transaction requires its own selling price to establish the outcome. The example supplies no early-sale proceeds; its maturity payment cannot substitute for them.431

For bills held in TreasuryDirect, maturity brings a choice between redemption and reinvestment. Redemption returns the money to the holder. Reinvestment buys another bill of the same term, with its rate fixed at its own auction. Choosing the same term does not carry forward the original rate or lock in future returns.54

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