What the Bank Discount Rate Measures
Treasury bills, commercial paper, and bankers' acceptances are zero-coupon instruments issued at a discount and redeemed at face value. There are no periodic interest payments — the entire return is the spread between what you pay today and what you receive at maturity. The bank discount rate annualizes that spread so paper of different maturities and sizes can be quoted on a single scale.
The convention divides the dollar discount by face value rather than by your purchase price, and it annualizes on a 360-day year. A $10,000 bill bought at $9,750 with 182 days to maturity carries a $250 discount, which works out to 4.95% on the bank discount basis. Dealers quote secondary-market T-bills exactly this way, with bid and asked expressed in discount-rate terms.
The quoted rate is a pricing convention, not your return. On that same bill the holding period return is $250 earned on $9,750, or 2.564% over roughly six months. Annualized on a 365-day basis that equals 5.14%, which is why this calculator shows money market yield and bond equivalent yield beside the headline figure. Quote paper on the discount basis; compare it on the bond equivalent basis.
The Discount Rate Formula Step by Step
Three inputs drive the math: face value, purchase price, and days to maturity. The dollar discount is D = FV − P. The bank discount rate is d = (D / FV) × (360 / t). On the default figures: D = 10,000 − 9,750 = 250, then 250 / 10,000 gives a 2.5% period rate, and 0.025 × 360 / 182 = 0.0495, or 4.95% annualized.
The 360/t factor annualizes the period rate. The bill runs about half a year, so the annualized figure lands near double the period rate. Shorter paper gets a bigger multiplier: 360/91 ≈ 3.96 for a 13-week bill and 360/28 ≈ 12.86 for a 4-week bill, while a 52-week bill multiplies its period rate by less than one.
Two conventions quietly depress the number. Dividing by face value ignores that you actually invested the smaller purchase price, and the 360-day year spreads the return over fewer days than a calendar year contains. The money market yield corrects the first problem: (250 / 9,750) × (360 / 182) = 5.07%. The bond equivalent yield corrects both: (250 / 9,750) × (365 / 182) = 5.14%.
Discount Yield vs Money Market Yield vs Bond Equivalent Yield
Three yield conventions describe the same instrument. The bank discount rate uses face value and 360 days. The money market yield, also called the CD equivalent yield, uses purchase price and 360 days. The bond equivalent yield uses purchase price and 365 days. Each step moves the number higher, and the ordering never changes: discount rate below money market yield below bond equivalent yield for any bill bought under face value.
On the default 182-day bill the three reads are 4.95%, 5.07%, and 5.14% — a 19.7 basis point spread between the quoted rate and the bond equivalent figure. The gap widens with maturity and with the level of rates. On longer or deeper-discount paper it can exceed 40 basis points, enough to flip a ranking against a CD or a coupon note if you compare on the wrong basis.
For cross-instrument comparisons, the bond equivalent yield is the industry standard because it puts discount paper on the same footing as semiannual coupon bonds. The bond equivalent yield calculator covers that conversion in detail, and the APY calculator handles the compounding side when savings products quote annual percentage yield instead.
Reading a Treasury Bill Quote and Deriving Price
US Treasury bill quotes in the secondary market are discount rates, not prices. A dealer asking 4.80% on a 182-day, $10,000 bill will accept price = 10,000 × (1 − 0.048 × 182 / 360) = $9,757.33. The asked rate sits below the bid rate — the reverse of coupon bonds — because a lower discount rate means a higher price for the buyer.
Auction results work the same way. The Treasury publishes a stop-out discount rate and winning bidders pay the derived price. A 4.30% rate on a 28-day bill prices it at $9,966.56 per $10,000 face, while 4.75% on a 91-day bill prices at $9,879.93. The price you enter in the calculator should match this derivation whenever you are verifying a quote before settlement.
Yield-to-maturity logic for coupon bonds follows a different route, discounting a stream of semiannual payments, which is why bill math stays simpler and cleaner. The bond price calculator shows the full coupon-bond version of present value pricing, and the bond current yield tool isolates the income component when you want to weigh coupon paper against discount paper.
Commercial Paper and Other Money Market Instruments
Commercial paper is quoted on the same discount basis as Treasury bills: maturities out to 270 days under the SEC 3(a)(3) exemption, face values starting at $25,000, and spreads that run roughly 20 to 100 basis points above comparable bills depending on the issuer's rating tier. A1/P1 paper trades tight against bills; lower tiers price wider. This calculator treats commercial paper identically — face value, purchase price, days to maturity.
Bankers' acceptances, agency discount notes, and dealer-placed bills all follow the same quoting convention. Because these instruments carry no coupons, yield-to-maturity machinery only applies to the coupon side of a portfolio — the discount leg is priced with the exact formulas this tool runs. The bond yield to maturity framework covers the coupon side for direct comparison.
Money market funds hold this paper in bulk and quote a 7-day SEC yield calculated on a bond equivalent basis. That figure is what belongs beside your calculator output, not the raw discount rate printed on the instrument. When a fund's 7-day yield sits clearly below the bond equivalent yield of bills you could hold directly, the management fee spread is the usual explanation.
The Other Discount Rate: DCF and WACC
In corporate finance the same term means something different: the rate used to discount future cash flows back to present value. That discount rate is usually the weighted average cost of capital or a required return built from a risk-free base plus risk premiums. It is an input assumption inside a valuation model, not a quoted market price on traded paper.
The two meanings connect at exactly one point — the risk-free anchor. The T-bill yield is the classic base rate in CAPM and build-up methods, so the output of this calculator feeds directly into the valuation-side discount rate. When analysts need that side of the chain, the DCF calculator discounts projected cash flows, and the cost of capital calculator builds the WACC that drives it.
Search results mix the two meanings freely, so confirm which question you are actually asking. If you hold or are buying short-dated paper and need the rate implied by its price, you are on the bank discount side and this calculator is the right tool. If you need to value a project, property, or company, you want the WACC-driven rate from the valuation side instead.
Comparing Short-Term Yields Fairly
Discount quotes, coupon yields, and APYs are not directly comparable figures. Convert everything to one annualized basis with the same day count before ranking anything. A bill quoted at a 4.95% discount rate delivers a 5.14% bond equivalent yield, which beats a CD at 5.00% APY by roughly 14 basis points — a win that is invisible if you compare the raw quotes and see 4.95% against 5.00%.
Taxes shift the ranking further. Municipal notes and tax-exempt funds quote yields that need grossing up before they can sit beside taxable bills in a comparison. The taxable equivalent yield calculator performs that conversion, and the compound interest calculator shows what rolling bills month after month does to realized returns versus a quoted simple rate.
Maturity matching matters as much as basis matching. A 4-week bill rolled eight times and a 182-day bill held once carry different reinvestment risk even at identical bond equivalent yields. Shorter paper gives up yield when the Fed cuts; longer paper locks the rate in. Laddering across 4-, 13-, and 26-week maturities smooths that exposure — the same principle fund managers apply inside money market portfolios.
Common Mistakes With the 360-Day Convention
The most common error is treating the quoted discount rate as the return. It understates yield for two stacked reasons: the face-value denominator (a $250 discount on $10,000 face is a 2.5% period rate but 2.564% on the $9,750 actually invested) and the 360-day year (worth about 1.39% in relative terms). Both corrections push the true annualized rate upward.
Day-count mistakes come next. Counting from the trade date instead of settlement (T+1 for bills) overstates the days and drags the annualized rate down. Using 30/360 bond-style months instead of actual calendar days distorts short paper badly — three days of error on a 28-day bill is more than 10% of its entire life, and the annualized figure inherits that distortion.
Mixing conventions across a comparison list produces quiet ranking errors — a 4.95% bill shown against a 5.00% coupon note loses on paper but wins at a 5.14% bond equivalent yield. Pick one basis, convert every instrument to it, then rank. The ROI calculator frames holding-period returns in general terms, while this tool keeps the money market day-count conventions straight.