How Fast the Interest Cost of the Federal Debt Reprices

Two numbers, published by two different parts of the U.S. government, sit more than a percentage point apart.

The Treasury reports that the average interest rate across all interest-bearing federal debt was 3.447% at the end of July 2026. The Federal Reserve's H.15 release for 25 August 2026 puts the ten-year Treasury yield at 4.64% and the two-year at 4.17%. The government is paying, on the whole stock of what it owes, well under what the market is currently charging on new money.

The comparison is not quite like for like, and the ways in which it is not are the interesting part. One number is a month-end average across every security outstanding, including debt issued a decade ago at coupons that no longer exist in the market. The other is a single day's quote on new money.

That gap is not an anomaly and it is not a mistake in either figure. It is what a stock looks like when it is measured against a price. What is worth measuring is how fast the first number moves toward the second, because that pace is the schedule on which higher yields turn into higher federal interest costs.

What the Average Rate Is Measuring

The Treasury's series is an average across every outstanding interest-bearing security, weighted by what is outstanding. A thirty-year bond issued in 2016 carries its 2016 coupon until it matures, and nothing the market does in 2026 changes that.

So the published average is a property of the stock — the accumulated pile of past issuance — while the market yield is a property of the flow, the debt being priced right now. Only two things move the stock toward the flow: securities maturing and being refinanced at current rates, and genuinely new borrowing.

The distinction is easiest to see in a deliberately artificial case. Suppose market yields doubled tomorrow and stayed there; suppose no security matured for a year; and suppose no new borrowing took place and no outstanding security carried a rate that resets. Under those three conditions the published average would not move at all, because nothing repriced. Actual debt fails all three conditions. The third is worth confirming rather than assuming: the same Treasury series lists Treasury Floating Rate Notes as a category of its own, carrying an average rate of 3.948% at 31 July 2026, alongside non-marketable categories including Government Account Series. Rates that reset without anything maturing are inside the number. Each condition that fails is a separate channel through which the average can move, and the published figure does not say which one is moving it.

This has a consequence that runs in both directions and is often only stated in one. The inertia that delays the arrival of higher interest costs would equally delay relief if market yields fell. The average is slow, not sticky in a particular direction.

Fourteen Readings, 14.3 Basis Points

The monthly series makes the pace legible.

• June 2025 — 3.304%, the low point of the period shown
• January 2026 — 3.316%
• July 2026 — 3.447%

From the June 2025 reading to the July 2026 reading — fourteen monthly observations, thirteen months apart — the average rate paid rose 14.3 basis points. Measured over the twelve months from July 2025 to July 2026, the rise was 9.5 basis points.

One limit on this article should be stated before the arithmetic goes any further. The market yields used throughout are from a single business day, 25 August 2026. This article has no series for where yields sat during the fourteen months above, and makes no claim about that path. Every comparison below is between a monthly stock average and one day's market quote.

Two details in that series are worth more than the headline. The first is that it fell for part of the period, from 3.372% in August 2025 down to 3.316% in January 2026 — a decline of 5.6 basis points over five months. What produced that decline is not in this data. The composition of what matured, the coupons it carried, what replaced it, and how much new borrowing was added on top are all outside a published average, and this article does not establish which of them did the work.

What the detail does establish is what the series is not. A declining average is not a report that borrowing got cheaper. It is a weighted average of coupons outstanding, and a weighted average can fall through more than one channel — through what leaves it, through what is added to it, or through components whose rate resets without anything maturing at all. Reading a market conclusion off it requires knowing which channel moved, and that is a different dataset.

The second is that almost all of the increase is recent. From January 2026 to July 2026 the series moved from 3.316% to 3.447%, which is 13.1 of the 14.3 basis points in the final six months of a fourteen-month window. The pace is not constant, and a single trailing figure conceals that.

How Much of the Stock Actually Repriced

The pace figure invites one more division, and it is the one that turns a rate into a quantity.

If the average rate paid rose 9.5 basis points over twelve months, and the securities doing the lifting were repriced to something near current market yields, then the share of the stock that moved can be approximated by dividing the change by the size of the step each repriced dollar took.

Two assumptions are inside that sentence and both matter. The step is measured from the current average of 3.447%, not from where the average stood a year ago; using the earlier figure would widen each step and shrink each implied share. And it treats the whole 9.5 basis points as coming from refinancing, which sets genuinely new borrowing at zero — the second of the two channels named earlier. Neither assumption is true, and the numbers below are illustrative bounds rather than estimates.

The answer depends entirely on where the refinancing landed, and the range is wide enough to be the point:

• Against the ten-year yield, a step of 119.3 basis points — implied share repriced, about 8% of the stock in a year
• Against the two-year, a step of 72.3 basis points — about 13%
• Against the three-month bill at 3.71%, a step of only 26.3 basis points — about 36%

Three plausible assumptions about where debt was refinanced produce answers that differ by more than four times. That spread is not a defect in the arithmetic; it is the arithmetic reporting honestly that a single rate cannot tell you about a quantity.

It also points at what actually governs the pace. Debt refinanced into bills barely moves the average at all, because bills are priced closest to it. Debt refinanced into ten-year paper moves it four times as hard per dollar. The composition of what is issued, not the level of yields, is doing most of the work — and the composition is not visible in either of the two published numbers this article started with.

The Gap, and What the Pace Says About It

Here is the arithmetic neither agency publishes, because neither is in the business of comparing its number to the other one's.

The gap between the ten-year market yield and the average rate paid is 4.64 − 3.447 = 1.193 percentage points. Against the two-year it is 0.723 points.

Divide the first by the trailing twelve-month pace of 9.5 basis points a year and the answer is about 12.6 years. Against the two-year gap, about 7.6 years.

It is worth being explicit about what the division does and does not assume. It assumes the pace of the last twelve months, which is one observation of a quantity that has already been shown to be unstable within the same fourteen-month window. It does not assume anything about the size of the debt, about revenue, or about policy. It is the gap divided by the most recent measured rate of closing, and nothing else is inside it.

Those numbers are descriptions of a pace, not forecasts, and the distance between those two things is the whole caveat. Market yields will not hold still for twelve years. The maturity profile of what rolls off changes every year. The pace itself accelerated sharply in the last six months of the series and could accelerate further or reverse.

The lag matters for reading almost any commentary about rates and the budget. A sentence of the form "higher yields are raising the government's interest costs" is describing something true and something slow at the same time, and the two get compressed into one tense. On this data the compression is worth more than a decade. A yield move in August 2026 enters the average through securities that mature and are replaced, on a schedule set years ago by when those securities were issued.

It also cuts against the reverse reading. If yields fall, the same schedule applies, and the relief arrives on the same delay. Neither direction is fast, and the asymmetry people often assume — costs rise quickly, relief comes slowly — is not in this series. What is in the series is a single slow mechanism running in whichever direction the flow points.

What the figure does establish is scale. Whatever happens to yields from here, the mechanism that converts them into federal interest expense is measured in years, not quarters. A market move this month does not show up in the average this month, and the arithmetic puts a number on how much it does not.

Where This Doesn't Apply

Several boundaries sit around the figures above.

• This is a rate, not a bill. The average interest rate says nothing about the size of the debt it is charged on. Total interest expense is that rate multiplied by a stock that is itself changing, and this article does not touch the second term.
• The comparison mixes two dates. The Treasury figure is a month-end value for July 2026; the market yields are a single business day in late August. Both are the most recent published, and they are not simultaneous.
• "Total interest-bearing debt" is a specific series. It includes marketable and non-marketable securities together, and the non-marketable portion does not price off the market at all. A comparison restricted to marketable debt would produce a different gap.
• The 12.6 years assumes one thing that will not happen. It holds the market yield fixed. If yields fall, the gap closes from the other side and the arithmetic overstates the time; if they rise, it understates it.
• Nothing here is about policy. Whether the pace is good, bad or manageable is a separate question that requires the size of the debt, the path of revenue and a view about growth. None of those appear above.

What to Watch Next Week

• The next monthly update to the Treasury's average interest rate series. The August 2026 figure will show whether the sharp six-month acceleration continued or was a rolling-maturity effect that has passed.
• Whether the two-year and ten-year yields hold near 4.17% and 4.64%. The gap is defined against these; the market side of the comparison moves daily while the Treasury side moves monthly.
• The shape of what is maturing. The pace of repricing is a function of how much rolls off and what coupon it carried, not of the yield level alone.

Concrete Framework

1. Take both numbers from their own source. Average rate paid from the Treasury's monthly series; market yields from H.15. Note the dates; they will not match.
2. Subtract to get the gap. Against the ten-year for a long-horizon read, against the two-year for a nearer one.
3. Compute the trailing twelve-month change in the average rate. This is the pace, and it is the number that is usually missing.
4. Divide the gap by the pace, then say out loud what the quotient assumes. It assumes the market holds still. Stating that turns the figure from a forecast into what it is: a measure of how slow the mechanism is.
5. Recompute the pace, not just the gap. The gap is watched constantly. The pace is what changed most in this data, and it is the term that decides how long anything takes.

Figures are from U.S. Department of the Treasury, Fiscal Data, "Average Interest Rates on U.S. Treasury Securities" (Total Interest-bearing Debt, through 31 July 2026) and Federal Reserve Statistical Release H.15 for 25 August 2026. Derived figures are arithmetic on those series and are not published by either source.