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Technical reference

Technical reference

Every stochastic component the model uses, written down: the distributions, the formulas, and the parameters behind them.

Engine 0.29.0Reviewed

This is the complete technical reference for the simulator’s model: every stochastic component it uses, set down with its distribution, its formula, and the parameters behind it. It assumes you are comfortable with the notation below. For the same ground in plain language, see How it works; for what the model deliberately leaves out, see Assumptions & limits.

1. How a simulation runs

The simulator follows one household across NN independent possible futures, year by year, from today to the last death in each future. Each path is its own roll of the dice: its own sequence of market returns, inflation, lifespans, and shocks. The numbers you see on the results page are summaries across all NN paths.

Every year runs through one cash-flow model: income and expenses meet, the portfolio funds any gap subject to a withdrawal rule, and, when money is tight, spending is cut. What distinguishes the years before retirement is a coverage assumption: your expense inputs describe your retirement plan, not your working-age budget, so pre-retirement the model injects a synthetic coverage income that closes the gap in normal times. The household is assumed to live off its earnings; only your stated contributions and one-off lump sums (an inheritance, a severance payment) are added to the portfolio. Steady income like rent is assumed consumed rather than auto-invested, because whatever you do save from it is already part of your stated contribution.

In a covered year the balance update therefore reduces to simple compounding plus new savings:

(1.1)

where CtC_t is the year’s contribution: entered in today’s euros, grown with inflation and any real raise, and (only when job-loss risk is enabled) paused in years the person is out of work. From retirement onward the coverage assumption ends. The expense inputs become the authoritative spending plan, and every income stream (pensions, rent, a still-working partner’s salary) offsets the drawdown, with any genuine surplus invested.

What happens each year

Within a single year, the model resolves events in a fixed order, because later steps depend on earlier ones (a death changes expenses; inflation sets the price level before costs are computed):

  1. Mortality: determine who, if anyone, dies this year.
  2. First-death transitions (couples): when one partner dies, permanently adjust the survivor’s expenses and pensions.
  3. Long-term care: test for the onset of a care episode, and age any episode already under way.
  4. Job loss: before retirement, test for an employment shock (only when job-loss risk is enabled; it is off by default).
  5. Inflation: draw this year’s inflation and advance the price level.
  6. Investment return: draw the blended portfolio return.
  7. Expenses: compute all seven spending buckets at this year’s prices.
  8. Income: compute all income streams.
  9. Withdrawal ceiling: the withdrawal rule proposes how much may be drawn.
  10. Spending cuts: if income plus the allowed draw cannot cover expenses, cut discretionary spending in priority order.
  11. Balance update: settle the year: subtract the net withdrawal, apply the return, add contributions and any surplus.

The rest of this reference takes these components one at a time.

2. Investment returns

The portfolio holds three assets (equities, bonds, and cash) in weights that sum to one. Its return in any year is the weighted blend of the three asset returns, less a flat annual management fee:

(2.1)

Allocation: fixed or glidepath

You can hold a fixed allocation (by default 60% equities, 40% bonds, 0% cash) or follow a glidepath, a schedule that shifts the mix as you age. Under a glidepath the equity share is read off a line through your chosen age-and-weight points: interpolated between them and held flat beyond the ends. Whatever is not in equities is split between bonds and cash in a fixed ratio (by default 80% to bonds). For a couple, the allocation follows the first person’s age.

The distribution of returns and inflation

Each year’s equity, bond, cash, and inflation outcomes are drawn together from one joint distribution, so they move in a correlated way: equities and inflation lean against each other, cash and inflation lean together, and so on. The distribution is defined by each variable’s mean and volatility and by the correlations between them.

Two shapes are available. The default is a multivariate normal: each outcome is its mean plus a correlated random shock,

(2.2)

where μ\mu collects the means and Σ\Sigma the variances and correlations. The alternative is a Student-t distribution, which keeps the same means and correlations but gives fatter tails: extreme good and bad years happen more often than the normal would predict. Its heaviness is set by a degrees-of-freedom parameter ν\nu (lower ν\nu = fatter tails); it is scaled so that the variances and correlations are preserved exactly.

Default market assumptions (annual)
ParameterDefaultMeaning
Equity return8% ± 17%mean ± volLong-run equity mean and volatility
Bond return4.5% ± 8%mean ± volLong-run bond mean and volatility
Cash return3% ± 3%mean ± volShort-term/cash mean and volatility
Inflation2.5% ± 3%mean ± volGeneral CPI mean and volatility (default model)
Management fee0.3%per yearFlat drag on the blended return
Default allocation60 / 40 / 0eq / bond / cash %Fixed allocation when no glidepath is set
Student-t tailsν = 6Degrees of freedom when fat tails are enabled (min 2)

3. Inflation: regime-switching

By default, inflation is one element of the joint draw above. An optional regime-switching model replaces it with something more realistic over long horizons: inflation alternates between a calm regime and a high regime, and persists in each.

A hidden two-state process governs which regime each year is in. From a calm year, inflation usually stays calm; from a high year, it usually stays high; occasionally it switches. The starting regime is drawn from the model’s long-run balance of the two.

(3.1)

Here pNNp_{NN} is the chance a calm year is followed by another calm year (default 93%) and pHHp_{HH} the chance a high year stays high (default 80%). Within each regime, inflation is drawn around a regime-specific average (calm around 2.2%, high around 7%) with its own spread.

(3.2)

Returns respond to inflation

The point of this model is that investment returns react to inflation. Once the year’s inflation is known, each asset’s return is drawn around its mean, tilted by how far inflation landed from its regime average:

(3.3)

The sensitivity ρ\rho differs by asset, and for equities it is stronger in the high-inflation regime (a deeper negative link) than in the calm one. In this mode the assets are tied to one another only through their shared response to inflation, rather than through direct asset-to-asset correlations.

4. Mortality

Each person’s age at death is drawn once, at the start of their path, from a Gompertz distribution, the standard actuarial shape in which the chance of dying rises roughly exponentially with age. The distribution is pinned by two numbers: a mode mm (the most likely age at death) and a dispersion bb (how spread out it is). Drawing a uniform random number UU and inverting the survival curve gives the years remaining:

(4.1)

with a hard cap at age 120.

The random number is drawn once, but the resulting age at death is not immutable: two in-simulation events can pull it earlier. Entering a care episode raises the death hazard for the episode’s duration (§6), and for couples the loss of a partner applies the widowhood adjustment below. Both work by re-solving the same survival curve with the elevated hazard. No new randomness enters, so comparisons across scenarios stay apples-to-apples.

The mode and dispersion come from country-specific life tables, by sex. Self-reported health then shifts the mode: better-than-average health pushes the likely age at death later, worse health pulls it earlier.

Gompertz parameters (mode, dispersion) by country and sex
ParameterDefaultMeaning
Greece (male / female)(84.6, 10.7) / (88.5, 9.9)yearsMost likely age at death, and spread
United States (male / female)(84.8, 9.5) / (88.2, 10.5)yearsMost likely age at death, and spread
Health adjustmentexcellent → poorShifts the mode earlier or later by self-reported health
Maximum age120yearsHard cap on any drawn lifespan

The widowhood effect

For couples, losing a partner shortens the survivor’s own expected life. In the year the first death actually occurs, the model brings the surviving partner’s age at death forward by a fixed amount, a deliberately simple stand-in for the well-documented spike in mortality after bereavement. The shift is on the order of one to two years for typical dispersions, and the survivor is always left with at least one more year than the partner who died first. If a bereaved survivor later enters a care episode, the care-driven recalculation of their lifespan (§6) is done first and the widowhood shift is then re-applied on top. That layering is a documented approximation rather than a joint model of the two hazards.

5. Couples

Correlated lifespans

Partners’ lifespans are not independent: shared environment, lifestyle, and age tend to make them die closer together than chance alone would suggest. The model captures this with a Frank copula, which links the two random draws that set each partner’s death so that they are positively associated, while still letting each partner’s age at death follow its own Gompertz curve. A single parameter controls how tightly the two lifespans are coupled.

What changes at the first death

A couple’s path moves through four states: both alive, either partner alone as the survivor, or both gone. The first death is a turning point, and the model makes three permanent adjustments to the survivor’s finances:

Expenses step down, bucket by bucket, because one person costs less than two, though not proportionally and not for everything:

Survivor expense levels after the first death (share of the couple's level)
ParameterDefaultMeaning
Essential60%of coupleFood, utilities, day-to-day basics
Discretionary55%of coupleTravel, leisure, non-essentials
Healthcare55%of coupleOne person's care rather than two
Housing100%of coupleUnchanged; see below
Long-term careper personAlready individual; not scaled

Housing costs are left unchanged after a death. A mortgage payment, property taxes, and maintenance on the same home do not fall just because one resident is gone, so the model holds them at the couple’s level rather than discounting them.

Pensions are reduced. Each partner’s pensions are personal: when a partner dies, their pension streams continue to the survivor only at the stream’s survivor share, while the surviving partner’s own pensions are untouched. The share the input step prefills is each country’s statutory rule resolved to an effective share for a typical dual-pensioner couple: Greece’s 70% halves once the survivor draws their own pension, the Netherlands pays no inheritance but raises the survivor’s own pension to the single rate, Sweden and Norway pass on nothing at all to retirement-age survivors. The per-country table in §10 lists every rule with its source.

Two countries follow a different mechanism entirely. In the United States and Ireland the survivor does not keep their own pension plus a share of the deceased’s; the household keeps the larger of the two main pensions. The model implements this directly: at the first death the deceased’s main stream is reduced so that the household’s main-pension income equals the larger of the two. For an equal-earning couple that means the survivor inherits nothing on top, which a fixed share would badly overstate. This computation uses the two entered amounts, so it is exact while both main pensions follow the same uprating path, which both countries’ price-linked rules satisfy; a manually diverged indexation makes it an approximation. Spousal top-ups paid while both partners are alive are not modeled.

6. Long-term care

Long-term care is modeled as its own spending bucket with its own onset, separate from ordinary healthcare. In any year, a person who is alive and not already in care can enter a care episode. The annual chance of onset rises with age along a Gompertz curve anchored at 65 and set slightly higher for women than men:

(6.1)

When an episode begins, its length is drawn from a lognormal distribution (a short-skewed shape: most episodes are brief, a few run for years), rounded up to whole years. While the episode is active, the long-term-care bucket carries that year’s care cost; when it ends, the bucket returns to zero. If the person dies mid-episode, both the episode and its cost end with them.

A care episode also raises the person’s mortality for its duration. Concretely: at onset, the person’s death hazard is multiplied by ×4 for the episode’s length, then returns to the normal age curve if they recover. Their age at death is re-derived under that elevated-hazard window from the same random draw that set it originally (a closed-form recalculation on the Gompertz curve of §4, not a re-roll). Someone drawn to die at 90 who enters care at 80 will typically die years earlier; someone who recovers from a short episode keeps most of their remaining life. Repeat episodes compound correctly. This matters for the headline number: without it, care paths would pay care costs over a full unshortened lifetime, systematically overstating cumulative care expense (the model’s scariest cost) and understating the chance of the money lasting for care-exposed plans.

By default the full market cost of care applies. If the family-care option is enabled, each episode is additionally tagged (with a country-specific probability) as one where family provides care, in which case a much lower cost applies for that episode instead.

What care costs, and who pays it

The cost of care is the single most country-dependent number in the model, and not because care is cheaper in some places. It is because the share of the bill that reaches the household differs enormously. In the United States a resident with savings pays the full private rate. In Denmark the care itself is free by law and what a resident pays is essentially rent and food. Those are not small differences of degree: they are the difference between a risk that can end a plan and one that barely registers.

Every figure below is what the household itself pays in a year, in today’s money and the country’s own currency, for a household that has retirement savings. That qualification does real work. Where help is means-tested, having savings is what disqualifies you from it, so the modelled household pays the full rate. Where care is funded for everyone against a capped fee, savings change nothing and the capped fee is what you pay.

What a year of residential care costs you, by country
CountryPer yearWho paysWhere the figure comes from
NorwayNOK 285,918The state funds the care. You pay a capped fee plus your room and meals.Lovdata / Helse- og omsorgsdepartementet (Norway)source
DenmarkDKK 188,400The state funds the care. You pay a capped fee plus your room and meals.Borne-, Aeldre- og Boligministeriet (Denmark)source
SwedenSEK 153,564The state funds the care. You pay a capped fee plus your room and meals.Socialstyrelsen (Sweden)source
United States$129,575You pay the full price until your savings run down far enough to qualify for help.Genworth Financial / CareScoutsource
New ZealandNZ$84,990You pay the full price until your savings run down far enough to qualify for help.Ministry of Health, New Zealandsource
SwitzerlandCHF 80,946Costs are split between the public system and you, by type of cost.Bundesamt fuer Gesundheit (BAG)source
AustraliaA$71,639Costs are split between the public system and you, by type of cost.Australian Government Department of Health, Disability and Ageingsource
United Kingdom£67,496You pay the full price until your savings run down far enough to qualify for help.Department of Health and Social Care (GOV.UK)source
Ireland€51,050You pay the full price until your savings run down far enough to qualify for help.Health Service Executive (HSE), Irelandsource
Germany€40,368Public care insurance pays a fixed amount by care level. You pay the rest.Verband der Ersatzkassen e. V. (vdek)source
Netherlands€36,742The state funds the care. You pay a capped fee plus your room and meals.CAK (Centraal Administratie Kantoor)source
Austria€34,776The state funds the care. You pay a capped fee plus your room and meals.oesterreich.gv.at (Republic of Austria, Bundeskanzleramt)source
Spain€27,961You pay the full price until your savings run down far enough to qualify for help.European Commission (Social Protection Committee / DG EMPL)source
Belgium€27,200Costs are split between the public system and you, by type of cost.Departement Zorg, Flemish Government (Belgium)source
France€25,968Costs are split between the public system and you, by type of cost.Caisse nationale de solidarite pour l'autonomie (CNSA)source
CanadaCA$25,550The state funds the care. You pay a capped fee plus your room and meals.Government of Ontario, Ministry of Long-Term Caresource
Finland€25,400The state funds the care. You pay a capped fee plus your room and meals.Pirkanmaan hyvinvointialue (Finland)source
Portugal€22,224You pay the full price until your savings run down far enough to qualify for help.OneValue, Government of Portugalsource
Italy€19,164Costs are split between the public system and you, by type of cost.Altroconsumo (Euroconsumers)source
GreeceNot publishedwe ask you insteadYou pay the full price until your savings run down far enough to qualify for help.No statistics office, regulator or ministry publishes one.
Amounts are what the household pays out of its own pocket in a year, in today's money and the country's own currency, for a household that has retirement savings. That last part matters: where help is means-tested, savings disqualify you from it, and where care is funded for everyone, your savings do not change what you pay.

The same figures, one country at a time and alongside everything else the model assumes there, are on your country’s page.

Why the model does not bill you the whole figure

Each of those charges buys a room and meals as well as care. Your plan is already paying for a roof and for groceries in its housing and essential spending, and the model keeps paying for both throughout a care episode. Billing the published charge on top would charge you twice for the same bed and the same dinner.

So the model bills the published figure minus what moving into care replaces, worked out from your own budget rather than a national average:

  • If you own your home, it subtracts your food and utilities only. You still owe the mortgage, the property tax and the upkeep on a house you are no longer living in, which is a real cost that people entering care genuinely carry.
  • If you rent, it subtracts your food and utilities and your rent, because the lease ends.
  • In a couple where one partner stays home, the housing is not touched. Only the partner in care stops eating at home.
  • Where family provides the care, nothing is subtracted at all. That care happens in the person’s own home, where they keep buying their own food and paying their own rent.

Where a country publishes a breakdown of its charge, that breakdown caps the subtraction, so the model can never credit back more living cost than the charge actually contains. Six countries publish one:

Published share of the care charge that is room, board and utilities
ParameterDefaultMeaning
Denmark100%Of the published charge
France91.53%Of the published charge
Sweden79.88%Of the published charge
Switzerland66.53%Of the published charge
Germany47.24%Of the published charge
Australia45.32%Accommodation is charged separately here, so rent is never subtracted

Australia is the exception that has to be handled by name: its published charge covers care and everyday living but not accommodation, which is billed separately. Subtracting an Australian household’s rent from it would discount the same thing twice.

Long-term care assumptions
ParameterDefaultMeaning
Annual cost of care€129,575 (US) / €25,968 (FR)today's money, per yearWhat the household pays while in care; see the table above for all twenty
Food and utilities share38.1% (US) / 66.33% (IT)of essential spendingThe part of your essentials a care home replaces
Family-care cost€3,000today's money, per yearApplied when family provides care (if enabled)
Family-care chance66.4% (GR) / 20% (US)Probability an episode is family-provided, when enabled
Mortality during care×4Multiplier on the death hazard while in care

Care costs rise each year with medical inflation, which runs above general inflation (see §8).

The full reference list

The source column in the table above carries one link per country, the strongest publication for the headline charge. The figures behind a country rest on more than that one page, so here is everything each country’s care model was built from, from the nursing-home fee itself down to the household budget survey that sets how much of your food spending a care home replaces.

Every publication behind the care figures, by country
Australia9 publications
Austria14 publications
Belgium11 publications
Canada8 publications
Denmark16 publications
Finland11 publications
France10 publications
Germany12 publications
Greece10 publications
Ireland12 publications
Italy9 publications
Netherlands11 publications
New Zealand7 publications
Norway12 publications
Portugal11 publications
Spain9 publications
Sweden11 publications
Switzerland12 publications
United Kingdom16 publications
United States20 publications
The table above links one source per country: the strongest publication for the headline charge. Each country's figures rest on more than that, including what the charge covers, the room and board share the model credits back, the chance that family provides the care, and health costs outside care. Open a country to see everything it was built from.

7. Job loss

Job-loss risk is opt-in and off by default. When it is off, it is fully off: no unemployment shocks are simulated and contributions are never scaled by employment state. When you switch it on, an after-tax employment income is required for every person still working. Unemployment is modeled as the loss of that income’s expense coverage: the year’s drain on the portfolio is your expenses minus whatever household income remains, capped at the lost salary. The unemployed year runs through the same withdrawal and spending-cut machinery as any tight retirement year.

With the toggle on, an earner faces an annual risk of losing their job before retirement. The risk rises with age, because older workers are displaced more often and re-hired more slowly:

(7.1)

When a shock hits, it is either permanent (about a third of the time), meaning employment and contributions stop for good in an early forced retirement, or temporary. A temporary spell lasts a short, randomly drawn number of years, during which employment income stops entirely, after which the person returns to work.

Re-employment carries a lasting penalty: wage scarring. Each temporary spell permanently reduces earning power by a fixed fraction, and repeated spells compound (two spells leave roughly three-quarters of the original wage). Permanent losses end earnings outright.

One caveat to know about: the drain uses your retirement-plan expense estimate as the working-age burn rate, because the model has no separate “spending while working” input. It is a documented approximation, not a bug.

Job-loss assumptions
ParameterDefaultMeaning
EnabledoffOpt-in; off means no shocks and no contribution scaling
Permanent share35%of shocksFraction of shocks that end employment for good
Temporary spell length~0.75years (avg)Average unemployment duration, rounded up to ≥1 year
Wage scar15%per spellPermanent earnings reduction on re-employment, compounding

8. Expenses

Spending is built from seven independent buckets, each computed at that year’s prices and then summed. Three inflation series drive them: general inflation, medical inflation (general plus a premium, default +1.8%), and home inflation (general plus a premium, default +0.5%).

Essential: food, utilities, and basics. Flat in real terms: it simply tracks general inflation.

Housing: either rent, which tracks general inflation, or ownership, which sums the mortgage payment (fixed in cash terms, ending when the mortgage is paid off), maintenance and property tax (each a fraction of the home’s value, which itself grows with home inflation), and home insurance (rising about 1% per year above general inflation).

Healthcare: a base cost at age 65 that grows with medical inflation and moves with age along a calibrated cost-by-age curve. The input step asks for this per person and counts it once per partner for couples; the figure it prefills is each country’s out-of-pocket healthcare spend per person at 65, on one defined basis: costs the household pays directly, including insurance premiums it pays itself, excluding anything already withheld from a pension before it lands, and excluding long-term care, which has its own bucket (§6). Published statistics rarely arrive on that basis, so each figure is normalized and the method recorded: figures published per household are divided by the official household size of the surveyed group, and figures published as all-ages averages are raised by the official age profile of health spending. This is why the prefill spans a wide range across countries: where premiums are withheld from pensions at source the direct figure is small, and where households pay premiums themselves it is large.

The curve itself is measured per country where a source exists. Fifteen countries carry their own, taken from the country’s household budget survey, its insurers’ administrative statistics or its regulators’ published rate tables, and the measured shapes disagree with the old one-curve-for-everyone assumption in a consistent direction: where the state caps patient fees or cover is priced the same at every age, a retired household’s own late-life spending rises gently into the early 80s and then levels off, and in Austria it measurably falls back after 80. Each curve’s source, arithmetic and open questions live in that country’s data file, and the publications behind it appear in the country’s reference list on the country pages. The five countries where no official source splits late-life spending by age (Norway, Sweden, Italy, Belgium and New Zealand) share a fallback curve calibrated so its late-life rise matches the US health accounts with long-term care removed; the evidence from their measurable neighbours suggests even that overstates them slightly, and the routes tried are recorded so the next attempt does not repeat them. In every country with its own curve, a couple’s healthcare is billed at each partner’s own age.

The United States has its own curve, and it falls at 65 and climbs again after. A retiree there buys their own cover until Medicare begins, at a premium the law prices by age, so the years just before 65 cost several times the years just after: the US curve carries that step exactly, billed at each partner’s own age for couples. After 65 the curve keeps rising, about a third by 95, because the top-up cover most American retirees buy alongside Medicare is priced by attained age in most policies; the slope is taken from four state insurance regulators’ published rate tables. The premium the pre-65 half prices is the full sticker price, and the government help with it is handled where the law puts it, in the tax bill: while household income stays under a cap the plan receives a credit against the benchmark plan’s premium, priced against every withdrawal decision, and one dollar of income above the cap removes the entire year’s help. The accounts step asks what the benchmark plan costs where you live, prefilled with the national average for your ages; the tax page records what the credit model simplifies.

What a retired household spends

The essential and discretionary prefills come from each country’s best retiree budget source: a published retirement budget standard where one exists, otherwise the national household budget survey’s retired-household tables. Every figure is decomposed into the app’s buckets, excluding housing and healthcare which are collected separately, and each country’s data file records exactly which survey categories went where.

Retired-household budget prefills by country: essential plus discretionary spending, single and couple, and healthcare per person at 65
CountrySingle, essential + discretionaryCouple, essential + discretionaryHealthcare at 65, per personWhere the figures come from
AustraliaA$2,552 + A$993/moA$3,452 + A$1,496/moA$2,365/yrsourceASFA Retirement Standard, Comfortable lifestyle, homeowners aged 65-84, March quarter 2026source
Austria€1,406 + €423/mo€2,109 + €635/mo (derived)€1,419/yrsourceStatistik Austria Konsumerhebung 2024/25, Einpersonenhaushalt 60 Jahre und aelter (monthly Verbrauchsausgaben, detailed results published 2026-03-04)source
Belgium€1,377 + €435/mo€2,066 + €653/mo (derived)€1,795/yrsourceStatbel Huishoudbudgetonderzoek (HBS) 2024, TAB04_BE group 'Alleen ouderen' (households consisting only of persons 65+), published 2 Sep 2025source
CanadaCA$1,290 + CA$530/moCA$1,936 + CA$795/mo (derived)CA$1,804/yrsourceStatistics Canada, Survey of Household Spending 2023: table 11-10-0227-01 (age of reference person 65+) decomposed by household size using table 11-10-0224-01 (household type)source
DenmarkDKK 9,750 + DKK 2,763/moDKK 18,469 + DKK 6,479/moDKK 8,271/yrsourceDanmarks Statistik Forbrugsundersogelsen, StatBank FU03 2022, enlig 60 ar og over uden born / 2 voksne hovedperson 60+ uden born (annual DKK per household incl VAT, current prices)source
Finland€612 + €48/mo€1,077 + €97/mo€1,100/yrsourceKohtuullisen minimin viitebudjetit 2025 (University of Helsinki / Kuluttajatutkimuskeskus reference budgets for a decent minimum, published 19.11.2025), single 65+ (man/woman averaged) and couple 65+, rest-of-Finland variantsource
France€1,035 + €335/mo€1,552 + €502/mo (derived)€1,691/yrsourceEnquete Budget de famille 2017 (Insee Resultats 'Les depenses des menages en 2017'), table TF102: depenses annuelles moyennes par menage, personne de reference 65-74 ans (all household sizes)source
Germany€935 + €319/mo€1,403 + €479/mo (derived)€523/yrsourceEVS 2023 (Einkommens- und Verbrauchsstichprobe), Konsumausgaben privater Haushalte, soziale Stellung der Haupteinkommensperson: 'Nichterwerbstaetige: im Ruhestand' (retiree households, all household sizes)source
Greece€597 + €101/mo€896 + €151/mo (derived)€1,096/yrsourceELSTAT Household Budget Survey 2024, one-person household aged 65+ (monthly purchases per household, COICOP 2018, English-edition tables T1.05/T1.10)source
Ireland€976 + €261/mo€1,293 + €391/mo€2,367/yrsourceMESL 2026 (Minimum Essential Standard of Living), Older Adult living alone / Older Couple, URBAN, Vincentian MESL Research Centre at SVPsource
Italy€896 + €110/mo€1,504 + €231/mo€1,234/yrsourceIstat Spese per consumi delle famiglie 2024, persona sola 65 anni e piu / coppia senza figli con p.r. 65 anni e piu (mean monthly EUR per household, COICOP 2018, published 2025-10-07)source
Netherlands€955 + €287/mo€1,604 + €470/mo€2,514/yrsourceCBS Budgetonderzoek 2020 (StatLine 83678NED amounts x 83679NED detailed shares), household types 'Alleenstaande man/vrouw vanaf AOW-leeftijd' and 'Paar zonder kind, vanaf AOW-leeftijd'source
New ZealandNZ$1,809 + NZ$666/moNZ$4,968 + NZ$1,225/moNZ$1,409/yrsourceNZ Retirement Expenditure Guidelines 2025 (Massey University NZ Fin-Ed Centre), Choices budget, Metropolitan, one-person and two-person householdssource
NorwayNOK 13,524 + NOK 1,080/moNOK 20,983 + NOK 2,160/moNOK 18,653/yrsourceSIFO Referansebudsjett 2026 (OsloMet, prices Feb 2026, 70+ rows), plus SSB Forbruksundersokelsen 2022 (StatBank 14227 single 65+, 14152 couple) for utilities, housing and healthcaresource
Portugal€511 + €120/mo€861 + €187/mo€757/yrsourceINE Portugal IDEF 2022/2023 (Inquerito as Despesas das Familias), agregado '1 adulto idoso' 65+ / '2 ou mais adultos pelo menos 1 idoso' (annual EUR per household, COICOP 2018)source
Spain€911 + €177/mo€1,367 + €266/mo (derived)€1,009/yrsourceINE Encuesta de Presupuestos Familiares (EPF) 2025, hogar de una sola persona de 65 o mas anos (COICOP 2018/EPF, annual EUR per household, published 2026-06-25)source
SwedenSEK 6,545 + SEK 1,200/moSEK 11,140 + SEK 1,810/moSEK 12,918/yrsourceKonsumentverket Hushallskostnader 2026 reference budget (71+ rows), plus SCB Boendeutgifter 2024 for housing and SCB HUT 2021 for healthcaresource
SwitzerlandCHF 1,440 + CHF 613/moCHF 2,729 + CHF 1,134/moCHF 7,290/yrsourceBFS HABE (Haushaltsbudgeterhebung) 2020-2021 pool, Einpersonenhaushalte ab 65 Jahren / Paare ab 65 Jahren ohne Kinder (mean CHF per household per month)source
United Kingdom£1,470 + £984/mo£1,921 + £1,475/mo£367/yrsourcePLSA/CRSP Retirement Living Standards, Moderate tier, outside London (2026 update, 'RLS 2025 uprated' budgets)source
United States$1,489 + $611/mo$2,686 + $1,283/mo$5,511/yrsourceBLS Consumer Expenditure Surveys, cross-tabulated Table 3600 (consumer units of one person by age of reference person) and Table 3620 (consumer units of two people by age), '65 years and older' column, 2023-2024 two-year averagesource
Essential and discretionary exclude housing and healthcare, which the app collects separately. Couple budgets marked derived apply a documented equivalence factor of about one and a half to the single budget; the rest are published couple rows. The standards are not one concept: some countries publish comfortable-retirement standards, others actual-spending survey averages, and each row names its own.

For the country-shaped view of these prefills, with their published basis spelled out, see your country’s page.

The free tier collects one number instead of buckets and splits it using per-country shares derived from the same budget data (the schema’s global split of 55% essential / 15% housing / 10% healthcare / 20% discretionary remains only as the fallback when a country supplies none).

Discretionary: travel and leisure. Tracks general inflation but tapers with age along an S-shaped curve, settling toward a floor as activity declines in later years:

(8.1)

with a floor ff (default 5%), a midpoint age amida_\text{mid} (default 80), and a steepness kk.

Long-term care: the care cost from §6, active only during a care episode.

One-off: planned, dated events (a new roof, a wedding), entered in today’s or fixed euros and applied in their year.

Family support: recurring help to family over a chosen age range, tracking inflation with an optional real growth rate.

Home equity as a last resort

For homeowners, the plan can treat the home as a final backstop. It is on by default, with a toggle on the Housing step. If a year arrives where income plus the entire remaining portfolio, after the tax that liquidating it would trigger, cannot fund the survival floor, the home is sold instead of the plan failing: the sale realises that year’s home value less a haircut (default 10%, covering transaction costs and the urgency discount), any remaining mortgage is settled out of the proceeds (its balance estimated as the present value of the remaining payments at an assumed 5% rate), and the rest joins the portfolio. From the following year the household rents: the rent equivalent defaults to the home’s value times a per-country gross rent yield (5% US, 4% GR), rising with general inflation, unless you set an explicit monthly rent instead. The plan counts as failed only if the floor is still unfundable after the sale.

The model is deliberately simple, and one-way. There is no buying back in, no downsizing or partial sale, no reverse mortgage; the home’s value follows its deterministic inflation drift, and the post-sale rent derives from the home’s value today rather than its (per-path) value at sale. Sale proceeds, once in the portfolio, are taxed like any other withdrawal when spent, which is conservative for a primary residence in most jurisdictions. Because the household sells only at the brink of insolvency, real households would typically act earlier; the fallback is a floor on how bad things get, not a strategy.

On the results page the sale shows up three ways: a sentence under the headline (“in X% of futures the home is sold, median age Y”), a marker on the portfolio chart at the median sale age, and a “plus home equity” note beside what’s left at the end. That figure itself stays portfolio-only. An unsold home is shown as context, never added to it.

Selected expense assumptions
ParameterDefaultMeaning
Medical inflation premium+1.8%per yearMedical inflation above general inflation
Home inflation premium+0.5%per yearHome-value inflation above general inflation
Maintenance1%of home / yrAnnual upkeep as a share of home value
Property tax0.3% (GR) / 1.2% (US)of home / yrAnnual property tax as a share of home value
Home-sale haircut10%of sale priceTransaction costs + urgency discount when the fallback sells the home
Post-sale rent yield5% (US) / 4% (GR)of home / yrGross yield deriving the rent equivalent after a fallback sale
Discretionary floor5%of baseLower limit the discretionary taper settles toward
Essential floor80%of baseMost essentials can be trimmed under stress

9. Spending cuts under stress

When income plus the most the withdrawal rule allows cannot cover the year’s expenses, the household trims spending. Not all spending can be cut, though, and the order matters. The model cuts in priority, taking as much as it can from each before moving on:

  1. Discretionary, down to its floor (a small fraction of the base).
  2. Family support, down to zero.
  3. One-off expenses, deferred or cancelled.
  4. Essential, down to its floor (by default, no more than a 20% trim).

Housing, healthcare, and long-term care cannot be cut: these are obligations. Whatever shortfall remains after exhausting the cuttable buckets is a forced shortfall: spending the household needed but could not fund. Because the floors above define the minimum the household can survive on, a forced shortfall arises only when a path has genuinely run out of money. It is the signature of a ruined year. For homeowners with the home-equity fallback on (§8), one more thing happens before that verdict: the home is sold, and ruin is declared only if the floor is still unfundable with the proceeds in hand.

10. Income

Each income stream carries its own basis: you say whether the amount you entered is before tax or after tax, and the model routes it accordingly (§12). “Real growth” always means growth above general inflation. The model tracks six kinds of income.

Employment: salary, growing with inflation plus a real raise, gated by whether the person is working and scaled by any wage scarring, and ending at retirement:

(10.1)

Pensions: up to four streams (each partner’s main and supplementary). Each begins at its own start age and is indexed one of five ways: by full inflation, by inflation plus or minus a fixed margin, by inflation capped at a ceiling, at a fixed annual rate, or by a custom schedule. Indexation begins the year after the pension starts; before the start age the entered amount is uprated with full inflation so it keeps its purchasing power.

The margin mode exists because most countries’ statutes are not plain price indexation: wage-linked systems and guarantee rules have historically run above prices, and some capped or conditional rules have run below them. The input step’s default, “as your country’s pensions do”, writes the researched rule for the selected country; the margin for each country is calibrated against its realized uprating history over the last fifteen to twenty-five years, and the evidence window is recorded in the data file. The default start age is likewise the country’s fully phased-in state pension age, not a global constant.

State pension rules by country: the default start age, how payments rise, and what a surviving partner keeps
CountryPension ageHow payments riseWhat the survivor keeps
Australia67With inflation, plus 0.8 points a yearsource33% of the deceased's pensionsource
Austria65With inflationsource40% of the deceased's pensionsource
Belgium67With inflationsource10% of the deceased's pensionsource
Canada65With inflationsource60% of the deceased's pensionsource
Denmark70With inflation, plus 0.5 points a yearsource35% of the deceased's pensionsource
Finland67With inflation, plus 0.2 points a yearsource25% of the deceased's pensionsource
France64With inflation, minus 0.4 points a yearsource54% of the deceased's pensionsource
Germany67With inflation, plus 0.2 points a yearsource55% of the deceased's pensionsource
Greece67With inflation, minus 0.5 points a yearsource35% of the deceased's pensionsource
Ireland66With inflationsourceKeeps the larger of the two pensionssource
Italy68With inflationsource60% of the deceased's pensionsource
Netherlands68With inflation, plus 0.5 points a yearsource46% of the deceased's pensionsource
New Zealand65With inflation, plus 1.0 points a yearsource30% of the deceased's pensionsource
Norway68With inflation, plus 0.3 points a yearsourceNothing passes onsource
Portugal68With inflationsource60% of the deceased's pensionsource
Spain67With inflationsource52% of the deceased's pensionsource
Sweden68With inflation, minus 0.4 points a yearsourceNothing passes onsource
Switzerland65With inflation, plus 0.3 points a yearsource30% of the deceased's pensionsource
United Kingdom68With inflation, plus 1.0 points a yearsourceNothing passes onsource
United States67With inflationsourceKeeps the larger of the two pensionssource
These are the values the input step prefills and the simulation executes. Rise labels compress each statute into the nearest rule the engine can run, calibrated against the country's realized uprating history; survivor shares are the effective share for a typical dual-pensioner couple, with income offsets noted in the data files.

Each of these rules is also explained in words, with its statute and sources, on your country’s page.

Supplementary pensions get none of these defaults: workplace and private schemes are contracts, so they start on plain inflation indexation with a neutral 50% survivor share, and your plan statement is the source that matters.

Rental: net rental income that grows with inflation plus real growth and is scaled by a constant occupancy rate; an expected maintenance cost (a fraction of a month’s rent per year, from the chance and size of repairs) subtracts from it. In extreme settings the net can go negative, and it is treated as a cash flow rather than floored at zero.

Lump sums: dated one-off receipts (an inheritance, a property sale), in today’s or fixed euros.

Other: any recurring income over a chosen age range, with optional real growth.

Selected income assumptions
ParameterDefaultMeaning
Real wage growth+1%per yearSalary growth above inflation
Pension indexation cap2%per yearCeiling when capped-inflation indexation is chosen
Rental occupancy90%Constant occupancy rate
Maintenance cost5% chance × 3 monthsper yearExpected repair cost, deducted every year in months of rent

11. Withdrawal strategies

In drawdown, a withdrawal rule sets a ceiling on how much may be taken from the portfolio each year. It does not generate spending. Your expense plan drives what the household actually spends; the rule only caps how much of it the portfolio will fund before spending cuts kick in. The model offers three ceilings; all are then subject to a survival override (below).

Constant-real (the “4% rule”)

The classic Bengen rule. The first year’s withdrawal is a fixed percentage (default 4%) of the balance at retirement, and that amount thereafter only keeps pace with inflation. It does not rise or fall with the portfolio:

(11.1)

Constant-percentage

A fixed percentage of the current balance each year. Spending rises and falls directly with the portfolio.

Variable percentage withdrawal (VPW)

Each year’s withdrawal is the share of the current balance that an annuity over the remaining horizon would pay out, given an assumed real return:

(11.2)

The assumed return rr is a blend of equity and bond real-return assumptions at the current allocation, so it drifts as a glidepath de-risks. The withdrawal share is capped from age 85 on. VPW spends more as the balance grows and pulls back when it shrinks, and rises naturally with age as the horizon shortens.

The survival override

Whatever the rule proposes, the household must still cover its hard floor, the irreducible minimum left after every allowed spending cut: floored essentials, all housing, healthcare, any care costs, and the discretionary floor.

(11.3)

If meeting this floor requires more than the rule allows, the model overrides the rule upward and takes what is needed. The actual withdrawal is therefore the larger of “what the rule advises” and “what survival demands,” grossed up for the tax the withdrawal itself causes (§12) and capped at the balance. A path is ruined in the first year its income plus its entire remaining portfolio cannot meet the hard floor.

One subtlety: the ceiling is stated after tax, so it caps what lands in your pocket, not what leaves the portfolio. The gross draw that clears a given ceiling is therefore the solution of g−[Tt(g)−Tt(0)]=Wtg - [T_t(g) - T_t(0)] = W_t, which §12 solves exactly rather than dividing by one minus a rate.

Withdrawal assumptions
ParameterDefaultMeaning
Initial rate4%Starting withdrawal rate for constant-real / constant-%
VPW assumed return5% eq / 1.9% bondabove inflationReturn assumptions above inflation in the annuity factor

12. Tax

Tax is computed inside the year loop, on that year’s actual position, against the rules of the country in the plan. It is not a rate applied to the draw. Twenty countries are modelled; the tax page sets out country by country what each one covers and what it does not.

The year’s position

Each simulated year builds one household position: every income stream at its stated basis (before or after tax, per stream), the portfolio split into three account kinds, its cost basis, this year’s asset mix and this year’s returns. From it a country rule produces two quantities:

  • CtbalC_t^{\text{bal}}, a charge on the balance, independent of every decision the household makes that year. Wealth taxes and assumed-yield charges live here. Eleven of the twenty countries have one.
  • Tt(g)T_t(g), the income tax at a gross withdrawal of gg, which is the whole household bill at that draw and not the increment over drawing nothing.

The two are billed differently, and the split follows from the order the year loop has to run in. A spending bucket must be known before the withdrawal is solved, which CtbalC_t^{\text{bal}} is and Tt(g)T_t(g) is not. So the balance charge becomes a genuine eighth bucket and the income tax is netted out of income, leaving the whole gap, ceiling, cuts and ruin chain in the after-tax terms it has always used. That is arithmetically the same as billing both, and it keeps the solve in one place.

The tax bucket is exempt from the spending-cut cascade (§9): you cannot cut your tax bill, and letting the cascade shave it would understate ruin. The figure reported on the results page is neither of the two above on its own but the whole household bill at the draw actually taken, which is the number you would recognise from a tax return.

The gross-up, solved exactly

The engine needs the inverse: the draw that leaves a required amount in hand. Two properties make it cheap. Marginal rates are always below 100%, so g−Tt(g)g - T_t(g) is increasing; and a tax scale is piecewise-polynomial, so the function is made of smooth segments.

(12.1)

Each country returns its own analytic Tt′(g)T_t'(g) alongside Tt(g)T_t(g), so a Newton step costs one evaluation rather than the two a numerical derivative needs. The slope between segment boundaries is not monotone (a realistic United States position has sixteen corners inside a 300,000 range), so plain Newton can alternate across a corner instead of converging. The solve is therefore bracketed, taking the Newton step when it stays inside the bracket and bisecting when it does not. Both ends of the bracket are free: the low end is a zero draw, already evaluated for the year, and the high end follows from the floor on the slope. Three iterations plus a final linear correction land exactly on a piecewise-linear segment.

Accounts, cost basis and the asset mix

The portfolio is split three ways, and the split changes the bill by more than any rate does.

Account kinds
ParameterDefaultMeaning
Tax-freeinvisibleNothing while held, nothing on withdrawal, and absent from every threshold. That last part is most of its value.
Tax-deferredordinary incomeNothing while held; the whole withdrawal is income in the year it is taken, unless the country charges it at a set rate instead.
Taxableas it arises, then on the gainDistributions or an assumed yield each year, then the profit portion on sale. The only sleeve where the asset mix matters.

Withdrawals are split across the three sleeves pro rata, in the configured proportions. Ordering, where a household empties one account before touching the next, is a real strategy and is not modelled; the reported bill is the neutral no-strategy case.

Cost basis is tracked rather than assumed: one per-path array, seeded from the starting portfolio, increased by contributions and by income taxed as it arises, and reduced pro rata on withdrawal. Crediting taxed income to the basis is not a refinement. The balance update compounds a total return, so distributions are implicitly reinvested; taxing them without crediting them would tax the same money again as a gain on sale.

Within the taxable sleeve, interest, dividends and gains are charged at the rates their country actually applies to each, using the plan’s asset weights.

What you hold inside that account can change the bill by more than any rate does, so where a country taxes two instruments differently, the Detailed view asks. Greece charges nothing on a European fund and 15% on a bank deposit. The Netherlands puts a savings account and a money-market fund in different statutory categories and charges them almost five times apart. Every menu is prefilled with the instrument that country’s own tax literature says people actually hold, so leaving it alone gives you the same answer as before the question existed.

Most countries are asked nothing, and that is a finding rather than a gap. A Dutch retiree can hold an Irish fund, an American one, a Dutch one or individual shares and the charge on their shares and bonds is identical, because it falls on what you hold and not on what it pays you. The United States is the same once both sides are counted: tax-exempt municipal bonds do cut the bill, but the market prices that exemption into a lower yield, and this model has no way to charge you the lower yield. Showing you one half of that trade would be worse than showing you neither.

Roth conversions (United States)

A premium United States plan can carry a conversion schedule: a yearly amount, in today’s money, moved from the tax-deferred sleeve into the tax-free one across a chosen age window. The move executes at the top of each simulated year, before that year’s tax context is built, and it is capped at what the deferred sleeve holds above the year’s required minimum, because the law makes the required withdrawal come out first. The moved amount is ordinary income in the year it moves and nothing else: it is not spendable cash, so the solver funds its tax with a correspondingly larger withdrawal, under whatever account order the plan uses. Everything downstream reprices on its own, because it all reads the same income: the taxable share of Social Security, the stacking of investment income, the deduction taper for 65 and over, the pre-65 health-cover help and its cap, the Medicare surcharge two years later, and every future required minimum, which shrinks because the account it is computed on shrank.

The five-year rule is charged. Money converted while under the access age skips the 10% early charge on the way in, and each year’s conversion then carries its own five-tax-year clock; taking converted money back out before its clock has run pays the 10% after all. The engine tracks each vintage separately, lets money out oldest first, and treats the Roth balance the plan started with, plus later contributions, as never clocked. All of these amounts are tracked in the money of the year they moved, deliberately: growth inside the Roth never shortens a clock. Two edges are approximate and both are disclosed where they bite: earnings drawn past every clocked and unclocked dollar before the access age owe only the 10% here, where the law would also income-tax them, and the deferred sleeve is assumed never to contain after-tax contributions, which where false overstates the conversion’s tax.

Two more deliberate positions. The schedule converts on every surviving, solvent path, crash years included: a real household might pause, but a schedule that quietly paused in bad years would make the comparison against not converting dishonest. And the product ships no optimiser and no fill-to-bracket mode: the cost of the next converted dollar is not monotone, so the results page draws the cost curve with its steps named and compares whole schedules on identical futures instead of asserting a stopping point.

Thresholds over time

Whether a bracket or an allowance keeps pace with inflation is researched per parameter and per year, not assumed per country: United States brackets are indexed while the thresholds that decide how much of Social Security is taxable have been frozen since 1983. Where a freeze has a statutory end date the projection uses it, so the United Kingdom’s personal allowance stands still through 2030/31 and then tracks prices, because the annual uprating duty is suspended for named years rather than repealed. The default follows the research. Two overrides let you stress it either way, assuming every threshold keeps pace or that none of them moves.

Tax settings
ParameterDefaultMeaning
Modecountry"country" uses the modelled rules; "flat" falls back to a single rate on the draw; "off" treats every amount as already after tax
Threshold indexationresearched"researched" follows each parameter's own history, including a statutory end date on a freeze; "full" and "frozen" are the two stress tests
Withdrawal orderproportional"proportional" draws a bit of each account by the configured split; "taxable_first" drains the ordinary account first and the tax-free pot last; "deferred_first" drains the tax-deferred account first. Enforced in the shared composition layer, so every modelled country honours every order
Flat-mode rate0%The override rate, used only when mode is "flat". Applies to the whole draw, not the gain
Assumed dividend yield1.6%The income share of the equity return, needed because dividends and gains carry different rates in most countries

13. Sensitivity analysis

Sensitivity analysis answers: of the things you could change, which ones move your outcome the most? It works by varying your inputs (starting portfolio, contributions, retirement age, and so on) within plausible bands around your actual plan, and measuring how much each one drives the variation in an outcome such as success probability.

The method is Sobol’ variance decomposition. Inputs are varied together using a low-discrepancy sampling design that covers the space efficiently, and the model reports two numbers per input. The first-order index is how much of the outcome’s variation that input explains on its own; the total-effect index adds its variation through interactions with other inputs:

(13.1)

A key technique makes this reliable: every input combination is evaluated against the same set of random market and lifespan draws, so the differences in outcome reflect the input change, not luck. Without it, the sensitivity signal would be drowned in Monte Carlo noise.

Three tiers vary more inputs at higher tiers, and the one your plan gets is chosen for you: the smallest set that still covers everything your plan actually uses. Nothing is asked of you here, and there is nothing to trade off. Inputs your plan leaves empty, such as a mortgage you do not have, are skipped rather than ranked, so they cost you no waiting and produce no empty bar.

Sensitivity tiers
ParameterDefaultMeaning
Low7 inputsPortfolio, contributions, retirement age, expenses, pension, care cost, equity weight
Medium10 inputsAdds withdrawal rate, where your savings sit, healthcare cost
High13 inputsAdds supplementary pension, wage growth, mortgage

14. Failure-mode attribution

When a plan fails, this analysis asks which risk caused it. It works by replaying each failed path with one risk at a time switched off, holding everything else identical, and checking whether the path now survives. A path that survives once a given risk is removed was, in part, sunk by that risk.

Five risks are tested, each neutralized in a natural way:

  • Long-term care: no care episode ever begins: the costs disappear, but so does care’s shortening of life (§6), so the “no care” path also lives longer. The channel measures the honest net effect.
  • Job loss: no employment shock occurs.
  • Longevity: nobody lives unusually long (lifespans capped at their typical value).
  • Market returns: returns replaced by their average.
  • Inflation: inflation held at its average.

Counting how often each risk rescues a failed path gives its share of the blame. Two further figures fall out: failures that survive only when two or more risks are removed are over-determined (no single fix would have saved them), and failures that survive even with every risk removed are structural: the plan was simply under-funded, not unlucky.

15. Counterfactuals

A counterfactual answers “what if you changed one thing?” and shows the effect on your plan. The model runs each change against the same random futures as your baseline, so the difference is attributable to the change alone, not to luck.

The changes are chosen for you, adaptively. The model takes the inputs that the sensitivity analysis found matter most, keeps those that map to an action you can actually take, and skips changes that wouldn’t apply (suggesting “save more” when you’re already retired, for instance). The standard levers are saving more each month, retiring later, shifting your equity weight, and insuring against care costs. Up to four are shown, ordered by how much they move your success probability.

For each, three differences from your baseline are reported:

(15.1)

The changes themselves are evaluated on the full model, so couples and every withdrawal rule are handled correctly.

16. Sustainable spending

This answers the planning question in reverse: how much could you spend each month and still hit your target success probability (90% by default)? Rather than reporting the success of one spending level, the model searches for the spending level that lands on the target.

It does so by bisection, repeatedly testing a spending level and then narrowing: if that level is still safe, try higher; if it fails, try lower; converge on the boundary. The search is bracketed first (does your current spending already pass, and is even zero discretionary spending fundable?), then halved a handful of times until the answer is pinned to within about €25/month. If even cutting discretionary spending to nothing cannot reach the target, the unavoidable bills already exceed what your income and portfolio can support, and the model says so rather than returning a figure.