Two Medicare late enrollment penalties are described the same way in almost every summary: sign up late, pay more for life. They are built on different units. The Part D drug penalty counts single months and multiplies them by a premium figure that the Centers for Medicare & Medicaid Services resets every year. The Part B medical penalty counts only completed twelve-month periods and multiplies them by a much larger premium. For 2026 the two base figures are $38.99 and $202.90. What follows is what each formula does with the same gap, and why one of them costs a different amount every January while the gap behind it does not change. What Starts the Part D Count The condition is not lateness in general. The Medicare drug coverage cost page states: “You may owe a late enrollment penalty if at any time after your Initial Enrollment Period is over, there’s a period of 63 or more days in a row when you don’t have Medicare drug coverage or other creditable prescriptio...
Treasury’s Daily Treasury Bill Rates table for September 3, 2026 lists the 26-week bill at 3.86 percent. A six-month certificate of deposit advertised at 4.00 percent APY looks higher by 14 basis points. The two figures are not measured on the same scale. One is a discount quote struck against par on a 360-day year; the other is an annual effective yield; and only one of them escapes state income tax. Converted onto a single scale, the same bill is 4.03 percent, and the state exemption moves the line a second time. What follows is the conversion, the statute behind the exemption, and the point at which a higher headline deposit rate stops winning.
One Bill Carries Three Different Rates
Two of the three are published side by side. The Treasury page that carries the daily series defines the first column this way: “The Bank Discount rate is the rate at which a bill is quoted in the secondary market and is based on the par value, amount of the discount and a 360-day year.” The next column is defined as follows: “The Coupon Equivalent, also called the Bond Equivalent, or the Investment Yield, is the bill’s yield based on the purchase price, discount, and a 365- or 366-day year.”
The arithmetic behind the September 3, 2026 quote runs in three steps. A 3.86 percent discount rate applied to a full 182-day term — the length of a twenty-six week bill at issue, rather than the days left to run on the particular bill being quoted — sets the price at 100 minus 3.86 times 182 divided by 360, which is 98.0486 per 100 of face value. The gain at maturity is 1.9514 per 100. Measured against the money actually paid rather than against par, that is 1.9903 percent earned over 182 days. Annualized on a 365-day year, it comes to 3.99 percent, which is precisely the coupon equivalent Treasury prints in the second column.
In dollars the same step is easier to hold onto. A bill with a face value of 10,000 dollars, quoted at that 3.86 percent discount rate, is bought for 9,804.86 dollars and pays 10,000 dollars at maturity 182 days later. The 195.14 dollars of difference is the entire return; a bill makes no interest payment along the way. Dividing that 195.14 by the 9,804.86 actually committed, rather than by the 10,000 the discount rate is struck against, is the whole reason the second column is higher than the first.
The third number is not published anywhere. Compounding the 1.9903 percent period return out to a full year gives an annual effective yield of 4.03 percent, a figure derived here from the Treasury quote rather than taken from it. That is the number that belongs beside a bank’s APY, because an APY is itself an annual effective rate. Between the quote a reader meets first, 3.86 percent, and the comparable figure, 4.03 percent, sit 17 basis points that no single published column displays.
The Spread Widens as the Term Gets Longer
The distance between the quote and the annual effective yield is not a fixed adjustment that can be memorized once. It grows with maturity, because the discount is taken against par on a 360-day year while the return is earned on a smaller price over a 365-day year, and because a longer holding period leaves more room for compounding. Treasury publishes seven maturity tranches, from four weeks to fifty-two. On September 3, 2026 four of them ran as follows: the 4-week bill quoted 3.70 percent, with a 3.76 percent coupon equivalent and a 3.83 percent annual effective yield; the 13-week bill 3.75, 3.84 and 3.89; the 26-week bill 3.86, 3.99 and 4.03; the 52-week bill 3.93, 4.11 and 4.15.
The spread between the first and the last of each trio widens from 13 basis points at four weeks to 14 at thirteen weeks, 17 at twenty-six weeks and 22 at fifty-two weeks. The 52-week row carries one additional wrinkle. Treasury notes that “The Coupon Equivalent can be used to compare the yield on a discount bill to the yield on a nominal coupon security that pays semiannual interest with the same maturity date.” That sentence states what the column is for, not how it is computed, and the Treasury page does not print the formula behind it. On a semiannual compounding convention the published 4.11 percent does reproduce from the September 3, 2026 price, and restating it as an annual effective figure adds about four more basis points on top of the discount-to-coupon adjustment. Both of those steps are this article’s calculation rather than Treasury’s.
The State Exemption Sits in a Statute, Not in Bank Policy
The comparison cannot stop at the yield, because federal and state treatment diverge. The exemption is not a courtesy extended by a broker or a bank. It is federal law, and 31 U.S.C. 3124(a) states: “Stocks and obligations of the United States Government are exempt from taxation by a State or political subdivision of a State. The exemption applies to each form of taxation that would require the obligation, the interest on the obligation, or both, to be considered in computing a tax, except— (1) a nondiscriminatory franchise tax or another nonproperty tax instead of a franchise tax, imposed on a corporation; and (2) an estate or inheritance tax.” The section runs to two subsections only; (b) is the last, and it hands the federal tax status of the same obligations to the Internal Revenue Code of 1986.
The Internal Revenue Service states the split in plain terms in Topic no. 403, last reviewed June 28, 2026: “This interest is subject to federal income tax but is exempt from all state and local income taxes.” Deposit interest carries no equivalent provision. It is ordinary interest income at both levels, and nothing in the rate a bank advertises changes that.
Because the federal treatment is the same on both sides, the federal marginal rate drops out of the comparison entirely. Both the bill and the deposit are taxed federally as ordinary interest income, so whatever bracket applies, it applies to each of them alike. Only the state layer differs, which is why a single variable, the state marginal rate, is enough to decide the ranking.
The separation is built into the information return as well. The instructions for Form 1099-INT direct the payer, for box 3, to “Enter interest on U.S. Savings Bonds, Treasury bills, Treasury notes, and Treasury bonds.” Certificate of deposit interest is not reported in that box. The two kinds of interest arrive on different lines of the same federal form before any state return is opened.
What a Deposit Has to Pay to Match the Bill
Once one yield is exempt from state tax and the other is not, the ranking is settled after tax rather than before it. If the state marginal rate is s, a certificate of deposit keeps 1 − s of its stated APY at the state level while the bill keeps all of it. Setting the two after-tax results equal gives the threshold directly: the deposit yield needed to match equals the bill’s annual effective yield divided by 1 − s. Using the unrounded 4.0314 percent behind the 26-week quote of September 3, 2026, the requirement climbs faster than the state rate itself. The figures that follow are calculated here and are not published by any agency. The 4.00 and 4.25 percent deposit rates used as examples are illustrative figures chosen to show the arithmetic; they are not survey averages, and they carry no date.
At a state rate of zero the deposit needs 4.03 percent, the identical figure, and the exemption is worth nothing. At 3 percent it needs 4.16 percent, at 5 percent 4.24 percent, at 7 percent 4.33 percent, and at 9 percent 4.43 percent. Expressed as the extra the deposit has to pay, that is 12, 21, 30 and 40 basis points respectively. Read in the other direction, an account advertised at 4.25 percent APY stays ahead of this particular bill only while the state marginal rate sits under 5.14 percent. Above that line the exempt yield wins, even though the bill’s annual effective yield is 22 basis points lower on the surface and its printed quote is 39 basis points lower.
The same threshold in dollars, on a 25,000 dollar position held for a year: the bill returns 1,007.86 dollars, all of it free of state tax. A deposit at 4.25 percent returns 1,062.50 dollars before tax, and a 5 percent state rate takes 53.13 of that, leaving 1,009.37 dollars. The deposit is still ahead, by about a dollar and a half, which is what a state rate slightly below the 5.14 percent crossing point looks like. Move the state rate to 6 percent and the deposit keeps 998.75 dollars, and the bill is ahead by 9.11 dollars on the same balance.
Numbers to Re-check
| Figure | Basis used here | Where to verify | How often it moves |
| 26-week bank discount quote, 3.86 percent | Secondary market, September 3, 2026 | Treasury, Daily Treasury Bill Rates | Every business day |
| Coupon equivalent, 3.99 percent | Same date, second column | Treasury, same table | Every business day |
| Annual effective yield, 4.03 percent | Computed here from that quote | Recompute from the current quote | Moves with the quote |
| State exemption for federal obligations | 31 U.S.C. 3124(a), text in force in 2026 | United States Code | Only by act of Congress |
| Federal taxability of bill interest | IRS Topic no. 403, reviewed June 28, 2026 | Internal Revenue Service | Reviewed periodically |
| Deposit APYs of 4.00 and 4.25 percent | Illustrative figures, not market observations | A specific institution’s disclosed APY | Set by each institution |
| Crossing points at 3, 5, 7 and 9 percent | This article’s calculation | Recompute with the current yield | Whenever the bill yield moves |
Where This Doesn’t Apply
- States with no individual income tax. Where the marginal rate is zero, the exemption changes nothing and the comparison collapses to 4.03 percent against the deposit’s APY. The same holds for a holder whose income falls below the state’s filing threshold.
- The exemption carries its own carve-outs. 31 U.S.C. 3124(a)(1) preserves a nondiscriminatory franchise tax or another nonproperty tax imposed on a corporation, and (a)(2) preserves an estate or inheritance tax. An individual holder is generally outside both, but an entity holding the same bill may not be.
- A federal deduction for state tax narrows the gap. A filer who itemizes and deducts state income tax bears less than the full marginal rate, so the effective
sin the formula is smaller. How much smaller depends on the federal bracket and on the limit that applies to the state and local tax deduction. - Both instruments are assumed held to maturity. A bill sold before maturity settles at whatever the market pays that day, and a deposit broken early is governed by the institution’s early withdrawal terms rather than by any yield formula. The one-year dollar figures carry a further assumption: that the twenty-six week bill is reinvested once at the same yield and that the deposit runs a full year at its stated APY. That is what an annual effective rate describes; the rate available at the roll is not known when the first bill is bought.
- A tax-deferred or tax-exempt account erases the difference. Inside an individual retirement account or a similar wrapper, neither the deposit interest nor the bill interest is reported on a current state return, so the exemption has nothing to act on and the higher stated yield simply wins.
- Deposit insurance is a separate question from yield. A certificate of deposit inside federal deposit insurance limits and a Treasury bill are not distinguished by any of the numbers above, and the choice between them is not only a rate comparison.
- The levels move; the arithmetic does not. The rates cited are indicative closing quotes for one business day, taken in the secondary market rather than at auction. The 17-basis-point conversion gap and the crossing formula survive a change in rates. The specific 4.03 percent does not.
This article explains how the rules are written and how the published figures convert. It is not tax, legal, or investment advice, and it does not account for any individual situation, state of residence, or filing status. Amounts, quotes, and thresholds change; verify the current figures at the sources named above, and consult a qualified tax professional before acting.
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