Abaque 10 · The geometry of withdrawal

The phase-out atlas

Three provisions built from one instrument: withdraw a benefit as income rises. They could all have been drawn the same way. They were not. Two are straight ramps that take the benefit away smoothly; the third is a staircase with cliffs, where a single dollar of income costs hundreds. Which geometry a provision got is a drafting choice, and this sheet is about where that choice fell — because the harshest geometry landed on the provision aimed at the lowest incomes.

Ramps2 of 3
Worst cliff—
You are in—
Implicit rate added—
Register—
Sheet10 · Rev A
Inputs

Enter the chart here

Filing status
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Your MAGI$26,000
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Age 50 or over
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Covered by a workplace plan
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Fig. 1

The atlas — three withdrawals on one income scale

Benefit remaining — ramp Benefit remaining — staircase Your MAGI
All three panels share one horizontal scale, so you can see not just the shape of each withdrawal but where on the income range it lives. They barely overlap: the Saver's Credit is finished long before the IRA deduction begins, and that is finished long before the Roth limit starts. The code withdraws these benefits in sequence rather than together — which is why no single income sits in more than one or two of them, and why the true marginal rate in Fig. 3 has separate humps rather than one tall one.
Fig. 2

The staircase in close-up — and the ramp that replaces it in 2027

Saver's Credit — through 2026 Lost at a single dollar Saver's Match — from 2027
Three vertical drops, each one triggered by a single dollar of AGI. The largest is the fall from the 50% rate to the 20% rate. Nothing about the policy required this shape — the IRA provisions in Fig. 1 do the same job with a ramp. And the point is proven by the statute itself: SECURE 2.0 repeals this credit after 2026 and replaces it with the Saver's Match, drawn here as the smooth line. That reform also makes the benefit refundable, which matters more than the shape — the 50% rate applies at the incomes with the least tax liability to offset, so the credit has always been largest exactly where it was least usable.
Saver's Credit now——
Next cliff——
Saver's Match, 2027——
IRA / Roth status——
Fig. 3

What the withdrawals add to your marginal rate

True marginal rate Ordinary bracket alone Added by the deduction taper
Only one of the three withdrawals produces a marginal rate, and it is worth being precise about why. The IRA deduction is worth cash, so losing it as income rises is an extra tax on each of those dollars — a genuine, calculable addition to your bracket. The Roth limit withdraws capacity, not cash: it costs you future shelter, not present tax, and adds nothing to this curve. The Saver's Credit produces no rate at all because a cliff has no slope — the loss is a fixed sum at one point, marked here in dollars rather than percent. Three withdrawals, three different kinds of cost, and only one of them shows up on a marginal rate chart. That is the trap: the other two are invisible here and still expensive.
Calculation

Every step, at your MAGI

Table 1

The three withdrawals side by side

ProvisionGeometryRangeWidth Full benefitWithdrawn per $1DriftWhat it costs you
Width is the distance over which the benefit is taken away. A ramp spreads the loss across that width; a staircase concentrates it at three points inside it.
Method, the three kinds of cost, and what is not modelled

The two geometries

RAMP benefit(m) = full × clamp((end − m) / (end − start), 0, 1) slope = full / (end − start) per dollar of MAGI STAIRCASE benefit(m) = rate(band containing m) × contribution slope = 0 everywhere, undefined at each boundary

A ramp has a defined slope everywhere, so it converts cleanly into an implicit marginal rate. A staircase has zero slope inside each band and an undefined one at the boundaries, which is exactly why its cost cannot be quoted as a percentage. The two are not variations on a theme; they are different objects.

Three withdrawals, three kinds of cost

  • Cash. The IRA deduction is worth its face value times your bracket rate. Withdrawing it is a real tax on the dollars that withdraw it: implicit rate = (full deduction ÷ band width) × bracket rate. On a single filer's $10,000 band that is 75–86 cents of deduction lost per dollar earned, so at 22% it adds roughly 17 to 19 points.
  • Capacity. The Roth limit costs no tax today. It removes future tax-free growth, which is real but is not a marginal rate and does not belong on Fig. 3. It is also the one withdrawal with a legal workaround: the income limit governs contributions, not conversions.
  • A fixed sum. The Saver's Credit cliff takes a specific number of dollars at a specific AGI. It has no rate. Quoting one would be arithmetic theatre — the honest unit is dollars, and this sheet uses dollars.

Why the ratios in the Saver's Credit bands are exact

The single-filer thresholds are exactly half the joint ones and the head-of-household thresholds exactly three quarters, because §25B(b) is written that way rather than indexing each separately. That internal consistency is a useful check on the figures: if a published table ever breaks those ratios, the table is wrong.

What the register records here

Nine entries, and the drift column is worth reading. The two married-filing-separately ranges are frozen at $0–$10,000 — never indexed since 1986 and 1998 respectively — so a punitive range becomes more punitive every year without anyone voting for it. The Saver's Credit contribution cap of $2,000 has been frozen since 2001, losing roughly 45% of its real value, which means the maximum credit has been $1,000 single and $2,000 joint for a quarter of a century. The band thresholds around it index annually. A provision can therefore be indexed and eroded at the same time, in different parts.

What is not modelled

  • Whether you can use the credit. The Saver's Credit is non-refundable, so the figure shown is a ceiling, not a payment. Many households in the 50% band owe too little tax to claim any of it. This sheet draws the statute, not the refund.
  • The backdoor Roth. The contribution limit is drawn as the statute writes it. Conversions are not income-limited, which is why the Roth ramp is routinely stepped around in practice — see sheet 09 for the five-year clock that governs the money afterwards.
  • Other phase-outs that share this geometry — the senior bonus deduction, the SALT cap phase-down, education credits, the ACA premium credit in sheet 07. The atlas is a sample, not a census.
  • State credits, several of which piggyback on the federal Saver's Credit and inherit its cliffs.
  • MAGI definitions. Each provision uses a slightly different one. They are treated here as a single figure, which is a simplification and occasionally a material one.

Confidence

All nine phase-out entries are Verified. The IRA and Roth ranges come from the IRS's own 2026 release; the Saver's Credit bands are corroborated against the statutory half and three-quarter ratios in §25B(b); the Saver's Match figures are from SECURE 2.0 §103 as enacted.

This is arithmetic, not advice. Dollar figures are approximate and re-indexed, and the ranges here move every January except the frozen ones the sheet marks. The Saver's Credit shown is a maximum before the non-refundability limit, which for many households reduces it to nothing. Whether a contribution is deductible, and whether a credit is usable, depends on facts this sheet does not have — take it to a CPA.
Indexed figures are re-set every January and this snapshot will go stale. Get notified when they are re-verified → · All twelve sheets