What we found

We set out to build a better engine for simulating investment returns, and found that the engine barely mattered. What mattered was UK tax law, the State Pension, and one decision about tax-free cash that moves the answer further than any other choice on this page.

Along the way the most famous number in retirement planning fell over. That seems the right place to start.

1The 4% rule is a fact about American data

The rule is familiar even to people who have never read where it came from: a retiree takes 4% of the pot in the first year, increases that amount with inflation every year after, and the money is said to last thirty years.

It comes from a 1994 paper by the American financial planner William Bengen. He took US market data going back to 1926, put a portfolio half in shares and half in bonds, and worked out what withdrawal rate would have survived every thirty-year window in that history. The answer was about 4%. His words: “In no past case has it caused a portfolio to be exhausted before 33 years.”

That is a real result, carefully done. But look at what it is a statement about. It is a count of overlapping windows drawn from one country's market history. It is not a probability. There is no sense in which it says “this works 100% of the time” — it says “this happened to work in every stretch of American history we have data for”.

Which raises an obvious question, and someone has answered it.

The same test, run on seventeen countries

In 2010 Wade Pfau ran Bengen's exercise across 17 developed countries using the Dimson–Marsh–Staunton dataset, covering 1900 to 2008. He allowed each country the best possible asset allocation with a century of hindsight, which is generous in a way no real retiree could be.

Four countries out of seventeen reached 4%. The United States was the fourth of them, and only just. A British retiree, drawing on British market history, would have got 3.77%. At a full 4%, the worst British starting year — 1900 — ran dry after 26 years.

What our own engine says

We tested the same withdrawal against a simulated market that compounds at 4.09% a year after inflation, with 16.5% volatility. A 4% draw survived thirty years in 74% of runs.

We want to be careful about what that does and does not show. It is not a replication of Bengen: our series is more volatile than his half-bonds portfolio and it is synthetic rather than historical, and both of those push the number down. It is a demonstration of something narrower and, we think, more useful — that the relationship between the draw rate and the rate the money actually compounds at is very nearly the whole story. A 4.00% draw from something growing at 4.09% is a close-run thing. The 100% was never a property of the number 4. It was a property of the data.

And all of that is before a penny of tax. Which is where the rest of this page comes in, because Bengen's American retiree was not navigating the UK personal allowance taper.

2“A 5% return” is not yet a number

Ask what a 5% expected return means and there are two answers. They are not close, and almost nothing tells you which one is meant.

If 5% is the geometric mean — the rate the money actually compounded at, year after year — then volatility around it does not much hurt the middle outcome, and can help it.

If 5% is the arithmetic mean — the simple average of the yearly returns — then volatility eats into it, and the more volatile the series the more it eats. This is not an obscure effect. Push volatility to 25% and a stated 2.94% real return compounds at −0.23%. The number on the page has not changed. The money is gone.

At the settings this calculator loads with, that single word is worth 12.3 percentage points of the headline: the same scenario funds the full income in 35.7% of runs reading the return as a geometric mean and 23.4% reading it as an arithmetic one. It is the second-largest row in the table in §3, and it is a choice this tool presents and measures rather than making silently on the reader's behalf.

The FCA's projection rates in COBS 13 Annex 2 are maximum rates set for a single-path, deterministic projection: a rate compounded annually, with no distribution around it. Nothing in the rules says what to do with that number inside a stochastic model, and the arithmetic/geometric distinction is never addressed there because within a single path it never arises. Where a tool does not say which convention it is using, the number it reports is ambiguous by construction. This tool makes the choice explicit, because the choosing is the modelling.

And the rate is a cap, not a recommendation

One thing about those rates that we had wrong ourselves until we re-read the Handbook. COBS 13 Annex 2 does not prescribe the return a firm must project. It sets a maximum: the firm's intermediate rate "must accurately reflect the investment potential" of the underlying investments and "must not exceed" 5% nominal for a personal pension. Only the inflation figures are fixed values.

So the 2.94% real this tool starts with is not a figure the regulator asserts is correct. It is the highest intermediate rate a firm is allowed to use, and a firm using it is supposed to be able to justify it against the actual investments. It is the cap on the central case, not the top of the permitted range — a compliant projection also shows a lower and a higher case, 2% and 8% nominal, and both are in the dropdown.

Deflating by 2% inflation, incidentally, is not a choice this tool made: the Handbook requires the projection to be in real terms and to use the intermediate inflation rate to get there.

3The decisions that move the answer are not the ones people model

We ranked modelling choices by how far each one moves a single number: the share of runs in which a £500,000 pot delivers £30,000 of income after tax from age 60 to 95. That is the scenario the calculator loads with: averaged over three random seeds it funds the full income in 35.7% of runs, and the single seed the front page uses reports 35%.

The last row is a matched pair rather than a change to the baseline: the same scenario run through a historical-style block bootstrap and through an independent lognormal draw, both set to the same 4.09% real return and 16.5% volatility, scored 46.0% and 48.8%.

That last row is the punchline. The return-generating engine — the part that looks like the hard modelling, the part with the interesting mathematics — is worth about a ninth of what happens to the tax-free cash.

We expected the opposite. The idea going in was that realistic market structure, with bad years clustering into bad decades, would separate a sophisticated engine from a naive one. It doesn't, and the reason is that daily turbulence largely washes out once it is compounded into annual returns. Matched on return and volatility, the two engines never disagreed by more than about three points anywhere on the withdrawal curve.

Three of the ten rows are specific to UK policy: the band freeze, the National Insurance record, and the treatment of the lump sum. We are not aware of a free calculator that models any of them.

Two of the rows are about charges, and they are worth reading together. Paying 0.75% a year costs more than retiring two years later gains. Paying 1.50% costs more than every other row here except spending the tax-free cash. Charges are modelled as exactly what they are — a deduction from the return — so it is no discovery that they behave like a lower return. What the table adds is the size of it in outcome terms, next to the decisions people actually spend their time on. The calculator ships with the charge set to zero, so every figure elsewhere on this page is before charges; the control is on the page and the figure that belongs in it is your own.

4The tax-free cash decision is the largest single choice on the page

A quarter of a pension pot can usually be taken free of income tax, subject to a lump sum allowance of £268,275. What happens to it next is, on these numbers, the largest single choice on this page — larger than the return assumption, larger than retiring two years later, and close to nine times the choice of simulation engine. (The household comparison in §5 is larger still, but nobody chooses their household.)

The mechanism is not complicated. In the model, a pound of retained lump sum displaces £1.25 of gross withdrawal at a 20% marginal rate and £1.67 at 40%, because it arrives without income tax attached. Spend it elsewhere and the taxable pot has to cover the whole income, at the taxpayer's marginal rate, for thirty-five years.

We are not saying what anyone should do with it — there are perfectly ordinary reasons to take the cash and use it, and this model knows nothing about anyone's circumstances. We are saying that if a projection does not ask the question, its answer is missing the largest term.

5Two of everything

Same £800,000, same £40,000 net target, same ages. The only difference is whether it sits in one name or two.

Nearly double the success rate and £94,000 less tax on the same delivered income, from nothing but having two of everything the tax system grants per person: two personal allowances, two basic-rate bands, two State Pensions.

The comparison has to be made on runs that delivered the income, because otherwise it flatters the wrong household. Across all runs the single person's median lifetime tax is only £181,200 — lower, but only because the median single-person run stops being able to withdraw at 83. Running out of money is an effective way to reduce a tax bill and a poor way to fund a retirement. We found this the hard way; §7 has the story.

Nobody can act on this — a household is not a setting. It is here because it calibrates the rest. An effect of 37 points makes the 12 points from the return assumption look modest, and makes the 3 points from engine choice look like what it is.

And the survivor cliff is the opposite of what people expect

The intuition is that losing a partner is a catastrophe for the pot. It isn't — because the survivor spends about a third less. What actually happens is quieter and worse.

Spending falls 33%. The withdrawal falls 4%.

The survivor loses one State Pension — £12,547.60 a year, which at the full new State Pension with no protected payment is not inheritable — and one personal allowance, £12,570 of tax-free room. Both vanish at once, and the pot has to replace them. So it drains for one person very nearly as fast as it did for two.

The cliff is real. It is a cliff in how efficiently income is produced, not in whether the pot survives. A model that reports only a success rate will show almost nothing happening. This one reports both.

6A bug in how this is usually built

GOV.UK presents income tax as ranges: £12,571 to £50,270 at 20%, and so on. That presentation quietly assumes a full personal allowance.

The legislation works differently. The basic-rate band is a width — £37,700 — that sits on top of whatever personal allowance survives the taper that begins at £100,000 of income. Once the allowance starts disappearing, the 40% band starts lower, not at £50,270.

Build a calculator from the published table rather than from the legislation and you understate the tax across the whole taper region. The gap widens as the allowance vanishes, reaching £5,028 a year — 40% of the lost allowance — the moment the allowance is gone at £125,140 of income, and staying there for every income above that. That is precisely the range a large pot in drawdown reaches when someone takes a big withdrawal.

Our first implementation had this bug. The engine now reproduces figures computed from the legislated rates exactly — £33,432 of tax on £110,000, £53,703 on £150,000 — and those two checks run every time the test suite runs.

Worth noting what kind of mistake it was: not an error in the mathematics, but an error in reading a government website correctly. Those are the ones that survive review.

7Two bugs in ours, and what they cost

The one the tests should have caught

In August 2026 we found that our Python engine handed a household £100,000 of tax-free cash out of the pot of a partner who was already dead when the projection began. A deceased member's lump sum entitlement dies with them; the pot passes across whole. Nobody could ever have taken that money.

On a £400,000 + £400,000 household with a £40,000 target and a partner dead at the start, the success rate was 90.1% before the fix and 88.1% after. Two points, in the flattering direction — just under the engine-choice effect in §3 that we use as the threshold for whether a feature is worth building at all.

The interesting part is why it survived. There are two independent implementations here, the JavaScript in your browser and a Python reference, and a script that cross-checks them against each other. The JavaScript had the guard. The Python did not. The cross-check should have caught it instantly — except that every couple test case passed a death age of zero. The comparison had never once exercised a death.

The fix and the tests that pin it are in the repository. We checked that the new tests fail when the guard is removed, because a test that cannot fail proves nothing. One of them is deliberately run at zero volatility, so the error shows up as a flat £100,000 discrepancy in the opening balance rather than as a statistical wobble a different random seed might have hidden.

The one we found writing this page

Checking the numbers for §5 turned up a second one, of exactly the same shape.

Lifetime tax was accruing on the withdrawal a household intended to make, not on the withdrawal its pot could actually fund. Once a pot ran dry the model went on charging tax to 95 on money nobody withdrew. The symptom, once we looked, was unmistakable: across 20,000 runs the lifetime tax figure took exactly one value. A run that failed at 83 and a run that paid out in full to 95 reported the same tax bill, and the number did not move when the returns did.

It survived for the same reason the first one did: nothing compared it. The browser engine does not compute lifetime tax at all, so the cross-check between the two engines had nothing to check it against. An output that only one implementation produces is an output no one is checking.

What it changed: the headline in §5 held up, because that comparison is made on runs that delivered the income in full, and on those runs the old figure was right. What was wrong was everything that depended on the spread — the claim that £111,450 was a median, and any comparison across runs that failed. The tax difference between one household and two moved from £94,275 to £94,260, which is to say it did not really move at all. The distribution behind it went from a single point to something with a shape.

The new checks in verify_household.py pin two things: that lifetime tax varies across paths at all, and that a run which ran out of money never reports more tax than one which funded the income in full. We removed each guard in turn to confirm the checks fail without it. The second check is the load-bearing one — the first can be satisfied by an engine that is still wrong.

8What isn't modelled

Being explicit about this matters more than the feature list.

• Inherited pots are treated as fully taxable drawdown. The real rules differ by age at death — broadly tax-free if the member died before 75, taxed at the beneficiary's marginal rate after. Ours is the cautious direction. It is a disclosed simplification, not an error — §9 has the rule at source.
• Only a partner's death is modelled, not your own.
• One tax charge is counted but not funded. When one partner's pot empties and the other covers the shortfall, the tax on that rescue withdrawal is recorded but not taken out of the donor pot. It makes the success rate very slightly generous, in a corner that only arises for couples once a pot is empty.
• Both pots in a couple share one return path. One household, one market — no diversification benefit between partners. Again the cautious direction, and stated on the page rather than buried.
• No National Insurance (correct for pension income, wrong the moment earned income is added), no money purchase annual allowance, no defined benefit pensions or annuities, no inheritance tax (§9 — the rules change on a date inside every projection here), and no care costs.
• Charges and ISAs are modelled, and this page said otherwise for longer than it should have. An ISA as a starting asset was added on 26 August and this list was not updated until 1 September; annual charges were added on 1 September. Both are controls on the calculator now. Unwrapped holdings outside a pension or an ISA are still not modelled.
• Mortality is a date you pick, not a probability.
• The State Pension defaults to the full new State Pension, which assumes a complete National Insurance record. Many people get less. An actual forecast is at gov.uk/check-state-pension.

9The pension and inheritance tax, from April 2027

For deaths on or after 6 April 2027, most unused pension funds and death benefits count as part of the estate for inheritance tax. That is sections 66 to 71 of the Finance Act 2026 — enacted, not proposed. The date falls inside the first year of every projection this page runs.

None of it is modelled here. Three facts about it that the tool does not use:

A surviving spouse or civil partner is still exempt

Pots passing to one are outside the estate on 6 April 2028 exactly as they were the day before, so the charge arrives at the second death rather than the first. The only death this tool models is a partner's death — which is the exempt one. Death in service benefits from a registered scheme, and dependants' scheme pensions from defined benefit or collective money purchase arrangements, are also outside the measure.

The income tax rules are unchanged, and still turn on age 75

A pot inherited from someone who died before 75 is broadly tax-free to the beneficiary, subject to the lump sum and death benefit allowance. From 75 onward it is taxed at the beneficiary's marginal rate. This tool treats every inherited pot as fully taxable, which is right after 75 and too cautious before it — see §8.

Where both charges land, they do not simply add up

Income tax is charged on the amount left after inheritance tax, not on the whole pot. On a death at 75 or over, in an estate above the nil-rate band, what reaches the beneficiary is:

40% inheritance tax, then income tax on the remainder. The widely quoted 64% combined rate is the higher-rate row, and it applies only where the member died at 75 or over.

Whether any of it is due at all depends on the whole estate — the nil-rate band is £325,000, the residence nil-rate band £175,000, and both are frozen until April 2030. This page knows nothing about the rest of your estate, so it cannot tell you which of those figures applies to you.

10The triple lock has been worth about 1.3% a year — and the 2.5% floor is not why

The calculator defaults to 0% State Pension growth above inflation, which is the assumption that the triple lock ends now. That default is unchanged, because what happens to the lock is a political question and not ours to answer. But it was an unexplained choice, and the size of the thing it switches off can be measured.

The triple lock uprates the State Pension by the higher of price inflation, average earnings growth, or 2.5%. So the growth it delivers above inflation is max(0, real earnings growth, 2.5% − inflation). Run that formula over ONS data for 2001–2025:

The two differ by 0.09 percentage points on the mean and agree exactly on the median, so the answer does not depend on which price index is used: about 1.3–1.4% a year in real terms. We give the range rather than one number because that is what the evidence supports.

For scale: §3 puts 0.75% a year of State Pension growth at +5.7 percentage points of success on the default scenario. The realised figure is roughly double that rate.

The 2.5% floor is the famous part and the smallest part

Public argument about the triple lock is mostly about the 2.5% floor — the leg that can raise the State Pension when both prices and wages are flat. Over these 25 years it was rarely the binding leg.

Earnings did the work. In a third of years the lock delivered nothing above inflation, because prices were rising fastest — which is the same mechanism that makes the lock worth least exactly when a pensioner needs it most.

What this does not show

• Twenty-five years is one policy era, not a long run. It contains the post-2008 real-wage stagnation and the 2022 inflation spike. A different quarter-century would give a different number.
• This is the formula, not the policy. The triple lock was only introduced in 2011 and was suspended for 2022–23. Applying it back to 2001 measures what the rule delivers on this data, not what pensioners actually received.
• Earnings here are whole-economy total pay, which is the series the uprating decision has used, but it includes bonuses.
• It says nothing about whether the lock survives. That is the question the slider exists to let you answer yourself.

11An undrawn pension is not hidden from the care means test

A common belief is that money left inside a pension is invisible to a local authority's financial assessment for care. Half of that is right, and the half that is wrong is the expensive half.

The fund itself is disregarded as capital — the Care and Support (Charging and Assessment of Resources) Regulations 2014, Schedule 2, paragraph 21. ISAs, cash savings and Premium Bonds are counted in full. But the Care and Support Statutory Guidance directs a local authority to impute notional income on a pot that is not being drawn, at the maximum income that could be drawn under an annuity product. Where income is being drawn, the assessment does not add the two together and does not net them off: it takes the higher.

So the income side of the assessment is a maximum, and leaving a pot alone imputes the maximum rather than nothing.

The size of it, from the government's own table

“The maximum income available under an annuity” is not a figure anyone publishes as a rate, but the Government Actuary's Department produces a table that measures exactly that quantity, and the guidance names GAD as a source of the estimate. On the table in force from 1 September 2025, a person aged 85 or over at a 4.5% gilt yield has a basis amount of £150 per £1,000 of fund — 15% of the pot a year.

On a £200,000 pot left undrawn at 85, that is about £30,000 a year of assessed income before the State Pension is added. The published worked example in the same document is for a 60-year-old and gives £62 per £1,000. At the ages when residential care actually starts the figure is more than double it.

Which means the two halves pull in opposite directions

Spending an ISA and leaving the pension alone reduces assessed capital and raises imputed income. Spending the pension and leaving the ISA does the reverse. No order of withdrawal is out of reach of both halves of the assessment.

Running the engine on a £300,000 pension beside a £100,000 ISA, £24,000 net a year from 60, and looking at the position at 85:

Spread across the four: £39,764 of lifetime income tax, and £105,283 on three years of care — running the other way. The order that pays the most tax pays the least for care, and the order that pays the least tax pays the most.

The success rate barely notices any of this. Measured separately, four orders differing by £158,280 of closing balance change the set of paths that last to 95 by between nought and two in twenty thousand. A single probability cannot carry a difference of £105,000, which is why this is written down here rather than added to the calculator.

Under local authority rules, spending your own capital on ordinary living costs is generally distinct from deliberately disposing of it. If a local authority decides assets were disposed of in order to reduce a care charge, it can assess the household as though those assets were still held.

And above roughly £350,000 of remaining pension it is worth nothing

Once the imputed income alone reaches the fee, the household pays the full cost whatever its capital looks like, and the order it drew money in stops mattering for care. Taking the State Pension into account, that point arrives at (£67,704 − £12,548) ÷ 0.150 = £367,709 of pension remaining. Because the GAD factor moves with gilt yields the boundary is a band rather than a point — about £340,000 to £395,000. On a household with £400,000 of pension and £200,000 of ISA, all four orders pay identical care costs for the first three years.

What this does not show

• The calculator does not model care at all. These figures come from running the engine directly, not from anything on the front page. The tool's headline numbers are unaffected by everything in this section.
• One deterministic household at 3% real, not a probability. No success rate should be read from this table.
• The care episode is indicative: real terms, no growth during the stay, the fee met from savings first and then the pension, the means test re-run each year. It establishes the direction and the order of magnitude.
• England only. Scotland's capital limits are £36,750 and £22,750 with free personal and nursing care; Wales sets a single residential limit of £50,000; Northern Ireland matches England.
• The fee is a self-funder rate. Councils block-purchase and pay less — the same source puts their median at £968 a week against £1,302.
• Nobody publishes how long people stay in care in a form this could use. Three years is an illustration, not an expectation. See §8.

Capital limits £23,250 and £14,250, tariff income £1 a week per £250, personal expenses allowance £31.80 a week: Department of Health and Social Care, Social care — charging for care and support 2026 to 2027: local authority circular, 17 February 2026. Notional income: Care and Support Statutory Guidance, Annex C, paragraphs 26(b), 26(c) and 35. Capital disregard: Care and Support (Charging and Assessment of Resources) Regulations 2014, Schedule 2, paragraph 21. Annuity maximum: HMRC and Government Actuary's Department drawdown pension tables effective 1 September 2025. Care fee: Personal Social Services Research Unit and Centre for Health Economics, Unit Costs of Health and Social Care 2025, published 1 June 2026, 2024/25 values.

12How to check any of this

Every figure on this page comes out of code that anyone can run.

git clone https://github.com/kdownie/uk-pension-stress-test
cd uk-pension-stress-test/engine
pip install -r requirements.txt
python verify.py && python verify_household.py && python verify_web.py

• verify.py — tax against figures computed from the legislated rates, the gross-up as an exact inverse of the tax function, the simulator against a closed-form answer at zero volatility, and the 4% result in §1.
• verify_household.py — Scottish bands hand-computed from the band table, couples, and the tax-optimal split checked against a brute-force search.
• verify_web.py — drives the actual live page in a headless browser and compares what the browser computes to what Python computes, line by line.

Every legislated figure lives in one block in engine/uk_rules.py with a source URL and the date it was checked. If a number is not there with a source, it is not used.

And you can check it without installing anything. The calculator will write you a CSV of one path, year by year, with volatility set to zero so that it is reproducible: opening balances for each of the three pools, what was drawn from each, the gross pension withdrawal, the income tax on it, and the growth applied. Every row can be recomputed from the columns beside it in a spreadsheet. The file is written by your browser and nothing is uploaded.

It is worth doing, because it shows you an approximation we would otherwise only have described. In the single year where retained tax-free cash covers part of the income, the engine scales the taxable withdrawal in proportion rather than re-solving the tax exactly — at the default settings that draws about £520 more gross than needed, in one year out of thirty-five. We have always disclosed that simplification. Now you can see it happen.

Monte Carlo figures move by a few tenths of a point between random seeds, so every simulated figure here is averaged over three seeds and quoted to one decimal place. The longer technical version of this page is docs/FINDINGS.md in the repository.

Sources

W. P. Bengen, “Determining Withdrawal Rates Using Historical Data”, Journal of Financial Planning, October 1994 — paper (PDF).
W. D. Pfau, “An International Perspective on Safe Withdrawal Rates: The Demise of the 4 Percent Rule?”, Journal of Financial Planning, December 2010 — paper (PDF).
Projection rates: FCA Handbook COBS 13 Annex 2 — handbook.fca.org.uk.
Tax and State Pension figures: gov.uk/income-tax-rates, gov.uk/new-state-pension.
Inflation and earnings (§10): ONS series D7G7 (CPI annual rate, dataset MM23) and series KAB9 and A2FD (average weekly earnings, dataset EMP), retrieved 31 August 2026. Contains public sector information licensed under the Open Government Licence v3.0.
Pensions and inheritance tax from April 2027: Finance Act 2026 (Part 2, sections 66–71), HMRC policy paper Inheritance Tax on unused pension funds and death benefits, HMRC technical note, and gov.uk/tax-on-pension-death-benefits for the age-75 rule.