On a Treasury bill, the bank discount rate and the coupon equivalent yield describe the same dollar return using different math, and the coupon equivalent yield is always the higher, more accurate number. A bill quoted at a 4.50% bank discount rate actually delivers roughly 4.61% on the money you put in. If you’re deciding between a T-bill and another investment, the coupon equivalent yield is the figure to use, because the bank discount rate systematically understates what you earn.
What Each Rate Measures
The bank discount rate is the quoting convention for short-term securities sold below face value, including Treasury bills, commercial paper, and banker’s acceptances.1sites.uni.edu. Bank Discount, Coupon Equivalent, and Compound Yields These instruments pay no periodic interest. You buy at a discount, receive full face value at maturity, and the gap is your return. The formula expresses that return as a percentage of face value, annualized over a 360-day year:
BD = ((Face Value − Price) / Face Value) × (360 / Days to Maturity)
The coupon equivalent yield, which the Treasury calls the “investment rate” in auction results, measures the same dollar return against the price you actually paid, annualized over 365 days.2TreasuryDirect. Price, Yield and Rate Calculations for a Treasury Bill For bills with 182 days or less to maturity:
CEY = ((Face Value − Price) / Price) × (365 / Days to Maturity)2TreasuryDirect. Price, Yield and Rate Calculations for a Treasury Bill
The bank discount rate is really a pricing tool. Given a face value and days to maturity, it translates directly into a dollar price, which is why dealers quote in those terms. The coupon equivalent yield is a return measurement, built on your actual capital and the actual calendar.1sites.uni.edu. Bank Discount, Coupon Equivalent, and Compound Yields
Why the Coupon Equivalent Yield Is Always Higher
Two independent distortions push the bank discount rate below the coupon equivalent yield, and they compound each other.
The first is the denominator. The bank discount rate divides by face value. The coupon equivalent yield divides by the purchase price, which is always lower for a discount security. Dividing the same dollar return by a smaller number produces a bigger percentage. This effect grows as the discount deepens, so longer maturities and higher rate levels widen the gap.
The second is the day count. Scaling from 360 days to 365 multiplies the annualized figure by 365/360, roughly 1.0139. That’s a constant lift of about 1.4%, regardless of the security’s price.
Neither rate accounts for compounding. Both treat each dollar of return as if it sits idle rather than being reinvested. For very short maturities this barely matters.
Converting Between the Two
You don’t need to work out the dollar price to move between the two rates. For bills maturing in 182 days or fewer, the algebra collapses to a single conversion:
CEY = (365 × BD) / (360 − (BD × Days to Maturity))
The numerator rescales from 360 to 365 days. The denominator shifts the base from face value to purchase price.
Worked Example: 91-Day Treasury Bill
Take a 91-day T-bill quoted at a 4.50% bank discount rate. Using the TreasuryDirect pricing formula, a $10,000 bill costs $9,886.25, so your discount income is $113.75.3TreasuryDirect. Understanding Pricing and Interest Rates
Convert the rate:
CEY = (365 × 0.045) / (360 − (0.045 × 91)) = 16.425 / 355.905 = 0.04614, or about 4.614%.
Verify by plugging into the CEY formula directly: ($113.75 / $9,886.25) × (365 / 91) = 4.614%. The numbers match because the conversion is just an algebraic shortcut for the same calculation.
p>That 11.4 basis point gap between 4.50% and 4.614% looks small. On a $1 million portfolio of T-bills it represents about $1,140 in annualized return you’d overlook by trusting the discount rate alone.
The Limit on the Simple Formula
The CEY formula above works only for bills maturing in half a year or less. For longer-dated bills, the Treasury uses a more complex formula that builds in semi-annual compounding, aligning the yield with the way coupon bonds pay interest every six months.1sites.uni.edu. Bank Discount, Coupon Equivalent, and Compound Yields
The reason is comparability. A Treasury note pays a coupon every six months, and its quoted yield assumes you reinvest at the same rate. To put a 52-week T-bill on the same footing, the calculation has to assume the same semi-annual reinvestment. The Treasury’s official formula for bills over 182 days solves a quadratic that bakes in this compounding.2TreasuryDirect. Price, Yield and Rate Calculations for a Treasury Bill
You rarely need to solve that by hand. Treasury auction results publish the investment rate alongside the discount rate, and most brokerage platforms display both. If you’re running numbers on a 26-week or 52-week bill yourself, know that the simple formula slightly understates the true coupon equivalent yield because it ignores compounding. The longer the maturity and the higher the rate, the larger that error.
Which Rate to Use When Comparing Investments
Treasury auction results report the “high rate” (the bank discount rate that set the price) and the “investment rate” (the coupon equivalent yield). The investment rate is always the higher figure.3TreasuryDirect. Understanding Pricing and Interest Rates
Brokerage statements vary. Some display only the discount rate because that’s the quoting convention. Others show the investment yield because it’s more useful for comparison. If you’re sizing up a T-bill against a money market fund, a CD, or a short-term bond fund, use the coupon equivalent yield. Comparing a bank discount rate to a bond yield mixes two different units of measurement.
The Tax Angle That Changes the Comparison
Discount income on a Treasury bill is taxed as interest, not as a capital gain, even though you buy at one price and receive a higher amount at maturity. That interest is subject to federal income tax but exempt from state and local income tax, matching the treatment of Treasury notes and bonds.4Internal Revenue Service. Topic no. 403, Interest Received
Brokers report short-term discount income on Form 1099-INT rather than 1099-OID, since T-bills mature within a year.5IRS.gov. Instructions for Forms 1099-INT and 1099-OID Under federal tax rules, discount on a short-term government obligation doesn’t accrue until the bill is paid at maturity, sold, or otherwise disposed of.6Office of the Law Revision Counsel. 26 USC 454 – Obligations Issued at Discount If you hold to maturity, you report the discount as interest income in the year the bill matures.
The state tax exemption matters when you’re cross-shopping. A T-bill yielding 4.6% on a coupon equivalent basis may beat a fully taxable CD at 4.8% once state income tax is accounted for, depending on where you live. Neither the bank discount rate nor the coupon equivalent yield captures that on its own; you need to layer the tax treatment onto whichever yield figure you’re comparing.