How it works

Why this exists

A retirement calculation that ends in a single large number says little on its own. The number is not the useful part. Which assumptions moved it is.

So this site shows return, inflation and tax as inputs you can change, and every projection is an estimate under assumptions you chose rather than a forecast.

Investment Path was built for people who want to understand a long-term saving plan before trusting its headline number. It keeps the assumptions visible, shows the arithmetic, and makes conservative comparisons easy without presenting an estimate as personal financial advice.

Built and maintained by Christoph Dirnbauer. The contact details are on the Legal notice.

Who built this

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The shape of the calculation

The simulation walks one month at a time, from today to the end of the plan. Nothing is computed yearly and then divided. At every monthly boundary, in this order:

1. the portfolio grows by that month's return;
2. while you are still saving, that month's contribution is added;
3. once retirement has started, that month's withdrawal is sold and taxed.

Contributions are paid at the start of each month, so the very first one is made today and earns a return in its first month. A 30-year plan therefore makes exactly 360 contributions, and the return on the last one lands on the boundary where saving ends and retirement begins. Those two phases share that boundary: the first withdrawal is taken there, not a month later.

Turning a yearly rate into a monthly one

Yearly return and inflation are converted to the monthly growth rate that compounds to the annual input:

m = (1 + r)^1/12 − 1

For a 7 % yearly return that gives m = 0.565415 % per month, and twelve of those compound back to exactly 7 %.

The shortcut of dividing by twelve is wrong and always overstates growth. 7 % ÷ 12 = 0.5833 % per month, and twelve such months compound to 7.229 % – about 0.23 percentage points of invented return every year. Over thirty years that is not a rounding error. The same exact conversion is applied to inflation.

A yearly raise is not converted at all. The increase of a monthly saving, of a fixed withdrawal and of a pension is one step on each anniversary of its phase, as a savings plan's Dynamik and a pension adjustment are: 300 a month rising by 3 percent a year pays 300 for twelve months and then 309.

Withdrawal percentages use a different depletion conversion. It makes twelve monthly withdrawals remove exactly the annual share:

d = 1 − (1 − r)^1/12

At 4 % a year this gives d = 0.339605 % per month. Simply dividing the yearly rate by twelve would remove only 3.9275 percent over twelve months, so it would understate the modelled annual depletion.

The month step, and a closed form

With m in hand, each saving month is two operations:

value ← value × (1 + m)
value ← value + contribution

Repeated n times with a constant contribution P, that is the standard future value of an annuity-due:

FV = P × [ (1 + m)ⁿ − 1 ] ⁄ m × (1 + m)

The trailing (1 + m) is the "paid at the start of the month" part; without it you would be modelling contributions that arrive a month late. The site does not use this formula – it runs the loop, because the loop also handles contribution changes, one-off events, tax and withdrawals, which no closed form covers. But the two agree to the cent on a plain plan, and the worked example below shows that check.

Inflation-adjusted values

Every figure is shown twice. Nominal is the euro amount at that future date. Real is the same amount after removing inflation:

real = nominal ⁄ (1 + i)ⁿ

where i is monthly inflation and n the months elapsed. At 2.5 % a year over 30 years the divisor is 2.097568, so a euro then buys what 48 cents buys now. Real is the honest number to plan with, and it is the one the site leads with.

Why the default is 2.5 %

It is a historically grounded planning assumption, not a forecast. The simple average of the published annual consumer-price inflation rates from 1950 through 2025, the latest complete year, is 2.47 %, or 2.5 % rounded to one decimal place. Figures through 1991 refer to former West Germany and later figures to reunified Germany; shorter periods can differ substantially.

Destatis historical review ↗ Destatis annual CPI ↗

How decision comparisons stay comparable

A comparison is valid only when both paths start with the same resources and every later euro has an owner. Each comparison therefore keeps an explicit timeline of deposits, loan payments, housing benefits, costs, withdrawals and outside cash. A balance may fall to zero; an unfunded cost may not disappear.

Winner language is shown only when timed cash contributions are equal. If they are not, the result reports the additional cash required and compares return measures without pretending the larger-funded path won on equal terms.

Mortgage results separate the contractual fixed-rate period from any continuation. A result after the fixed period exists only when a refinancing rate has been entered, and it remains a scenario rather than a lender offer or affordability approval.

Tax on gains

On a sale, tax is charged only on realised gains – not the full sale value. A German accumulating fund can also incur the Vorabpauschale explained below before any sale.

The German equity-fund default keeps the partial exemption, allowance and tax rate as separate steps. With no allowance left, the combined charge is equivalent to 18.4625 percent of a positive raw gain:

25 % Kapitalertragsteuer × 1.055 Solidaritätszuschlag = 26.375 %
fund income = positive realised gain × 70 percent
taxable income = max(fund income − remaining allowance, 0)
tax = taxable income × 26.375 percent

The order matters. The 30 percent Teilfreistellung reduces qualifying fund income first; the fixed euro Sparer-Pauschbetrag is subtracted afterwards. Folding the exemption into a rate before subtracting the allowance would shrink the allowance to 70 percent of its legal value. An asset that does not qualify uses a zero partial exemption. The Austria preset applies a simplified rate of 27.5 percent to gains realised on sale and uses an average cost basis.

It is not a full Austrian fund-tax model. It does not model ongoing fund taxation, reported distributions or distribution-equivalent income, nor the broker’s actual KESt withholding. Use it as a comparison assumption, not as an Austrian tax calculation.

Church tax is not simply added on

Kirchensteuer is charged on the Kapitalertragsteuer rather than on the gain, and it is itself deductible as a Sonderausgabe – so paying it lowers the tax it is charged on. That makes it a correction to the whole rate, not a number to add at the end:

KESt = taxable capital income ⁄ (4 + k)
total = KESt × (1 + 0.055 + k)

with k = 0.08 in Bavaria and Baden-Württemberg and 0.09 elsewhere. The equity-fund column below is the equivalent share of raw gain after the partial exemption when no allowance remains; the standard column applies to taxable income:

The intuitive arithmetic – 26.375 % plus nine, giving 35.375 % – overstates the bill by more than a quarter. Over a long drawdown that is not a rounding error, which is why the rate is computed for you rather than left as a sum to do in your head.

The yearly tax-free allowance

Germany's Sparerpauschbetrag (§ 20 Abs. 9 EStG) leaves the first slice of each year's investment income untaxed: €1,000 per person, €2,000 for a jointly assessed couple. The field takes any number, because it is a legal figure that has been changed before – it was €801 until 2023 – and a projection running to 2060 should not pretend otherwise.

Two properties make it behave unlike a rate:

• It is consumed. Once a year's sales have used it up, every later sale that year is taxed in full.
• It resets and does not carry over. An allowance you did not use is simply gone at the end of the year.

Where a realised loss has been banked, the loss is used first and the allowance absorbs only what survives. That is the order § 20 EStG prescribes, and also the one that wastes least: a banked loss keeps indefinitely, this year's allowance expires.

For a qualifying fund, the partial exemption is applied before the allowance. A €1,200 raw gain becomes €840 of fund income, so a still-available €1,000 allowance leaves no taxable amount.

The site charges it on calendar years, counted from the plan's starting month, so it renews each January; a plan starting in the middle of a year has a short first year with the whole allowance. Dated broker transactions can still give slightly different tax timing. Austria has no equivalent allowance.

Vorabpauschale: tax before anything is sold

A German accumulating fund does not distribute, so without a rule its holder would pay nothing for decades. § 18 InvStG closes that with an advance lump sum charged each January on the year just ended:

Basisertrag = base × Basiszins × 0.7
cap = max(year-end value − year-start value + distributions, 0)
Vorabpauschale = max(min(Basisertrag, cap) − distributions, 0)

The factor 0.7 comes from § 18 itself and is separate from the fund partial exemption. After the Vorabpauschale has been determined, the applicable partial exemption, remaining allowance and tax rate are applied in that order.

Two things keep it from running away. The total-return cap includes both price appreciation and distributions, so the same distribution is not subtracted twice, and the Zwölftelung gives each purchase only one twelfth of a year's Basisertrag for each month it was actually held – a December contribution accrues a twelfth, not the lot.

Whatever is charged raises your cost basis (§ 19 Abs. 1 S. 2 InvStG). That matters: without it, the same profit would be taxed once in advance and again when the share is finally sold. And since there is no cash account in a projection, the bill is paid by selling just enough – grossed up for the gain that sale itself realises.

The Basiszins is an assumption, not a constant. The BMF publishes it each January from the Bundesbank's 15-year government-bond yield: 2.55 % for 2023, 2.29 % for 2024, 2.53 % for 2025 and 3.20 % for 2026, which is the default here. It was negative in 2021 and 2022, and the charge those years was nothing at all. Over a thirty-year plan what you assume for 2041 matters far more than any figure yet published, so it is an editable input.

The charge is applied on calendar years: it falls due in January for the year just ended. For an accumulating fund, the base uses the value at the beginning of that year, its full-year return and acquisition-month weighting; a holding the plan starts with counts as held since January, valued at the plan's starting price. Credits follow the lots that generated them; a January contribution never receives the previous year’s credit. A distributing fund needs separate distribution cash flows and is outside this advance-tax model.

What it costs, in the same example

The plan below – €400 a month for 30 years at 7 %, with the €1,000 allowance – pays nothing at all for its first 10 years: purchases are valued at the January share price and weighted by acquisition month. Year one’s base is €2,547.15, so the Basisertrag is €57.06, and after the partial exemption the allowance covers it many times over. The first actual charge falls in year 11, and it is €33.56. By year 30 the portfolio is large enough that the year's charge is €1,650.47.

Over the whole thirty years €13,729.44 of assets are sold to settle it. The portfolio ends at €449,540.44 instead of €470,425.94 – but most of that gap is tax that would have been due anyway, just later. After settling everything, the plan is worth €410,827.92 against €410,423.30 without the charge.

So on this plan the charge leaves the investor €404.62 better off, and that is not a quirk of the arithmetic. Two opposite things are happening at once. Money taken early cannot compound, which is a real cost: set the allowance to zero and the same comparison shows the charge costing €14,246.47 over thirty years.

Against that stands the allowance, and it is worth being exact about how. It does not shelter the charge every year: it covers it completely for the first 10, and from year 11 onwards tax is really paid, which is how the thirty-year total reaches €13,729.44. What it does in those first years is convert an allowance that would otherwise have expired into cost basis, and every euro charged in any year raises that basis too, so the final sale is taxed on less. Across this plan the €1,000 allowance is worth €14,651.09 against the drag above, which is what turns the sum positive.

Which way it lands is an output of these inputs and not a rule. A portfolio large enough for the charge to outgrow the allowance early, a higher Basiszins, or an allowance already spent on something else all shift the balance back towards the lost compounding. Change the inputs and the same comparison will show you where it goes.

Which shares a withdrawal sells

Selling part of a portfolio means choosing which shares leave, and that choice changes the bill. Two methods are offered:

FIFO sells the oldest shares first, which is what German law prescribes for securities (§ 20 Abs. 4 EStG). Those are the shares that have grown the most, so they carry the largest embedded gain: early withdrawals are taxed harder, later ones more lightly. This is the default, because it is what actually happens.

Average basis applies the portfolio's overall gain fraction to every euro sold, as if every share were an average share. It is the usual projection shortcut, and it understates the tax on the first years of a drawdown.

One sale realises one gain: the proceeds minus the purchase cost of every share in it, netted with sign and only then floored at zero. That is how a single sell order is assessed, so a share now below its purchase price offsets an older share's profit within the same order rather than being ignored. A sale that nets a loss owes nothing and banks that loss against later gains, which is what the Verlustverrechnungstopf of § 20 Abs. 6 EStG does.

Getting a specific amount of cash

When you ask for a fixed sum – a monthly payout, a one-off withdrawal – the sale has to be big enough to leave that much after tax. Selling exactly the amount you want would leave you short by the tax.

Under the average method that is one division. Under FIFO it is not, because as the sale consumes older low-cost lots, the taxable fraction changes; it changes again if the running gain crosses zero. The required sale is solved piecewise, lot by lot, so the cash you asked for is the cash you get.

Which investment account is being modelled?

Fund gains and losses and share sales go through one account with one annual allowance. A loss can refund withholding paid earlier in the same tax year; unused losses carry forward, while unused allowances expire. A loss on direct shares stays in a pot of its own and only offsets gains on shares (§ 20 Abs. 6 Satz 4 EStG); any other loss offsets any gain, share gains included. Each year's Vorabpauschale is settled for every fund on the same day and paid from the funds that owe it, in proportion. Direct stocks receive no fund partial exemption or Vorabpauschale. Separate brokers would need separate accounts.

Each asset in a portfolio is taxed by the tax class the asset list records for it, not by the tax preset of the plan. Under the German fund rules an equity ETF keeps its 30 percent partial exemption, and a bond ETF has none, because § 20 InvStG grants one only to equity, mixed and property funds. Gold, silver and cryptoassets held directly are private sales under § 23 EStG: a gain is tax-free after a year of holding and otherwise taxed at the personal income tax rate. The projection has neither the holding period nor the personal rate, so a taxed plan holding them is refused rather than taxed as though they were a fund.

Retirement preserves each holding’s purchase lots, tax category and advance-tax credits. Sales are proportional across holdings and FIFO within each holding when FIFO is selected. This is a stated withdrawal policy, not a prediction of your broker’s orders.

A worked example, end to end

Every figure below is produced by the same engine that serves the simulator, on the same calculation version a fresh form submits, and a test recomputes them to keep this page honest.

Take a plan of €400 a month for 30 years, at 7 % nominal return and 2.5 % inflation, held in a German equity fund – so 26.375 % on income the 30 % Teilfreistellung has already reduced, with the €1,000 yearly allowance subtracted in between – followed by 25 years of drawing 4 %. Those are the simulator's own defaults, so you can reproduce every figure below by entering them. The Vorabpauschale is off, as it is on a fresh form; its own cost is worked out above.

Open this example in the simulator

1. The rates

return: (1.07)^1/12 − 1 = 0.565415 % / month
inflation: (1.025)^1/12 − 1 = 0.205984 % / month
drawdown: 1 − (1 − 0.04)^1/12 = 0.339605 % / month

2. The first four months

Month 0 is today: €400 goes in and has not yet grown.

Month 1 checks by hand: €400 × 1.00565415 = €402.26, plus the next €400, is €802.26.

3. After 360 months

The closed form agrees. Putting the same numbers through the annuity-due formula above:

400 × ((1.00565415)³⁶⁰ − 1) ⁄ 0.00565415 × 1.00565415 = €470,425.94

The month-by-month loop and the textbook formula match to the cent. That is worth stating because it is the one part of this page you can verify in a spreadsheet in two minutes.

The rest follows directly, and the order is the part worth following. The raw gain is what came out minus what went in: €470,425.94 − €144,000.00 = €326,425.94. The 30 % Teilfreistellung comes off that first, leaving €228,498.16 of fund income. Only then is this year's €1,000 allowance subtracted, leaving €227,498.16 taxable, and the tax is 26.375 % of it: €60,002.64.

Doing those two steps the other way round – folding the 30 % exemption into an 18.4625 % rate and then subtracting the allowance – is the mistake this page itself used to make. It is not a matter of rounding: an allowance is a fixed number of euros and a rate is not, so putting the rate first shrinks what the allowance shelters to seven tenths of it. Correctly ordered, the €1,000 takes €263.75 off the bill; the other way round it takes only €184.62. That is the whole of the difference between the €60,081.76 this page published and the figure above it – €79.12.

The inflation-adjusted value divides by the 2.097568 that 30 years of 2.5 percent inflation compounds to: €470,425.94 ÷ 2.097568 = €224,272.13.

Read those last two lines together, because they are the point of the whole exercise. The headline is €470,426. What it is actually worth, in money you can spend today and after the tax office has been paid, is €195,666 – 42 % of the headline. Any calculator that shows you only the first number is showing you the least useful one.

4. The first year of retirement

Drawing 4 % a year means selling 0.339605 % of the portfolio each month. On €470,425.94 that first sale is €1,597.59.

Under FIFO that sale takes the very oldest shares – the first month's contribution, paid in thirty years ago and now worth roughly eight times what it cost. So almost all of it is gain: €1,387.72 of the €1,597.59, or 87 %. The 30 % exemption brings that down to €971.40 of fund income, and a new plan year has just begun, so the whole €1,000 allowance is still there to cover it. Nothing is taxed at all: the full €1,597.59 is paid out, €761.64 inflation-adjusted, and €28.60 of allowance is left over.

The next month is the interesting one. The portfolio has grown, so the sale is slightly larger at €1,601.17 and its gain is €1,391.90, or €974.33 after the exemption. But the €28.60 left over covers almost none of it: €945.74 is taxable, the tax is €249.44, and the payout drops to €1,351.73. Nothing went wrong; the first month simply spent a year's allowance in one go.

That is why the site reports the first year's average rather than the first month alone: €1,379.38 nominal, €650.31 inflation-adjusted. Quoting €1,597.59 would advertise a monthly income the plan pays once every twelve months. The average is what it actually pays.

Notice that the portfolio keeps growing through retirement in this smooth scenario: 7 % growth followed by 4 % dynamic depletion leaves 1.07 × 0.96 − 1 = 2.72 % nominal balance growth over a year. That is a property of these inputs, not a law. Lower the return or raise the withdrawal and the same machinery will show you the balance falling.

Where the return comes from

The worked example uses a fixed rate. Three other modes are available, and they answer different questions.

Fixed applies the same return every month. It shows the shape of compounding clearly and says nothing about risk. Every number above is of this kind.

Historical replays a real monthly return series in order, oldest first. Returns are computed from monthly opening prices, adjusted for splits and for reinvested dividends, so they are total returns rather than price returns, and converted to euro at the exchange rate on each observation date. When a plan runs longer than the data – which most do – the geometric average of the part actually used carries the remainder. Because the series starts at a fixed point in history, a plan beginning at a market peak looks very different from one beginning at a trough. That sensitivity is the point of the mode, not a defect in it.

Monte Carlo draws each month's return randomly from a lognormal distribution whose expected return and volatility match your assumptions, runs many paths, and reports percentile bands. The 10th–90th band contains 80 percent of simulated outcomes under that assumed distribution. It is not an 80 percent guarantee about reality: real markets can produce extreme outcomes more often than this lognormal model assumes.

Your own holdings projects each named holding at its own assumption and sums them month by month, so a portfolio is not one average asset. It is deterministic like the fixed mode unless a market episode is placed on it.

In the guided planner a holding starts at a forward-looking return for its kind of asset: 7 % a year for a broad equity fund, the same figure the planner uses everywhere else, and 3 % for a bond fund, close to what long euro government bonds yield less fund costs. A single share, gold, a cryptoasset or a fund nobody has called diversified has no such figure, and you enter your own. The asset's own average over the history held for it, up to thirty years, is shown beside the field with the months it covers. It is context and not a forecast: a window that happens to hold one long rally would otherwise be projected for decades. The full simulator can still project a holding at that average, and says so on its row.

What each mode does differently

The four modes are one engine with four sources of monthly return, so the tax rules, the pension schedule and the advance charge are the same in all of them. Three things are not, and one of them used to be described wrongly on this site.

What the return means under volatility

Monte Carlo takes two numbers from you. 7 % is the long-run return a year, compounded: the rate a plan grows at over decades, the same one fixed mode uses and the one the rolling returns beside the field quote. 15 % is the standard deviation of single years' returns, an ordinary yearly quantity and not a logarithmic one. Reading it as one is the usual mistake, and it makes the simulation more volatile than the label says.

Each month is drawn from a lognormal distribution whose median path compounds at the return you entered. Writing m for 1 plus that return, s for the yearly standard deviation and G for 1 plus the expected return of a single year:

G² = (m² + √(m⁴ + 4 m² s²)) ⁄ 2
yearly log variance = ln(1 + (s ⁄ G)²)

At 7 % and 15 % that gives a log standard deviation of 0.138192 and an expected single year of 8.03 %, 1.03 % above the rate you entered. That gap is not an error and not a fee. A distribution that allows very good years places its average above its typical year, and the more volatile the assumption the wider the gap grows. Because the median path compounds at your rate, the middle line of the chart and a fixed projection of the same plan meet; what volatility adds is the spread around them.

Raise the volatility to 22 % at the same compound return and the expected single year rises to 9.15 %. The typical outcome stays where it was; the good and the bad years move further apart.

One warning about using that rate. The median of a whole plan is not this single-year median applied to the horizon: contributions, withdrawals and tax all interact with the path, so a plan's median outcome has to be read off the simulated distribution rather than computed from one rate. The percentile lines on the chart are the same reading taken month by month, which also means no single line is one simulated future – each point is the level that many separate futures came in below.

Where a plan owes a fixed amount every month, the result reports the share of simulated paths that delivered every one of them. That share is a property of these inputs, this horizon and this many paths, and it is not shown at all for a plan that withdraws a percentage of whatever is there: such a plan cannot run out in the same sense, and its risk is that the income falls, which the income percentiles show instead.

Where the numbers come from

Historical mode uses adjusted monthly opening prices for the selected index or security. Splits and reinvested dividends are included, and each observation is converted to euro before the monthly return is calculated. Prices are cached for a few hours rather than fetched per request.

Each monthly return is dated with the month it covers. The opening price of one month to the opening price of the next is that month's return, so a calendar year runs from the first price in January to the first price in the following January, and a period named from January to December holds exactly those twelve months. The long S&P 500 series below has one figure for each month instead of an opening price, so its return is dated with the later of its two months, and its calendar year runs from one December's figure to the next.

Because prices are converted to euro before returns are computed, a historical projection already carries the currency experience of a euro investor. All amounts on this site are shown in euros.

Series that reach further back than any fund

A tracking fund can only show its own lifetime, and the oldest one here begins in 1993, so the crash of 1973 and 1974 and the inflation that followed sit before its first price. A few series are therefore loaded from published datasets instead of being downloaded from a fund. They are always separate entries, never extra years spliced onto a fund's history, so no chart hides a join.

The S&P 500 series beginning in 1971 is built from Robert Shiller's monthly data, using his own total-return figures so that dividends are reinvested by his method rather than by a reconstruction of it.

Two things about it are worth knowing. Its figure for a month is the average of that month's daily closes rather than its last one, which slightly softens the highest and lowest points: across multi-year windows that makes no practical difference, but a one-year worst case reads a little milder than a month-end series would give. And before 1999 the euro did not exist, so the conversion uses the D-Mark at the rate fixed by law, 1.95583 to the euro, because a German investor in 1973 held marks and bore the dollar's fall in marks.

Why amounts are shown in euros

Amounts are shown in euros throughout the site. Historical returns include exchange-rate movements from a euro investor’s perspective, and the tax assumptions use German rules. Changing the interface language does not change the currency or convert amounts.

Everything else – return, inflation, tax rate, contribution, horizon – is an assumption you supply. None of it is forecast for you.

How statutory calculators are governed

A legal calculator names its jurisdiction, ruleset year, source and supported cases beside the result. Inputs that do not affect the selected legal path are hidden or explained; inputs needed for a correct result are never silently invented.

Unsupported combinations return a scope message instead of an authoritative total. Boundary tests cover thresholds, dates, ages, relationships and benefit months, while independent official examples are retained as versioned regression fixtures.

These results remain estimates. A tax assessment, Renteninformation, benefit decision, insurer statement or contract issued by the responsible institution is authoritative for an individual case.

How property is priced

A purchase price is not an acquisition cost. Transfer tax, notary, land registry and any agent share are spent on day one, are not lent against, and are included in the building and land allocation that the depreciation is calculated from. The first year of depreciation is prorated by the month of acquisition, and it stops once the building is written off: after fifty years at 2 percent.

A payment into a WEG maintenance reserve is cash leaving your account, and it is not deductible until the association actually spends it. Repairs are deductible when they are paid. The two are separate inputs because treating a reserve transfer as a repair overstates the deduction every year until the money is used.

A sale is modelled with its own friction: agent and transaction costs come off the proceeds. A let property sold within ten years of buying is taxed under § 23 EStG on its gain, measured from its cost less the depreciation claimed. The comparison lets the house for the whole horizon, so the exemption for having lived in it yourself in the year of the sale and the two years before does not arise there. A year's private-sale gains under 1,000 euros stay tax-free, which assumes the property is the only thing you sell that year. Owner-occupied use assumes no gain tax.

A German fixed rate usually ends long before the loan does, and nobody knows the rate that follows. Until you enter one, the property pages assume today's rate plus 1.5 percentage points: a stress test, not a forecast, named beside every result it moves. Empty the field and they withhold the verdict and every final figure that depends on it.

The mortgage page applies that rate over the loan's remaining term, so the payment changes. The ETF-or-property comparison sets its loan by an initial repayment, as banks quote it, so there the payment stays and the rate changes how long the loan runs.

A negative modelled tax is a potential loss offset and not a guaranteed refund: it depends on other taxable income, the loss rules and an accepted profit-making intent.

How pay is calculated

Payroll follows the year's official procedure, including the § 20 SGB IV transition formulas between the Minijob limit and €2,000 and the childless care surcharge from age 23. A Minijob is refused rather than estimated, because its pension election and flat tax are not inputs here.

Market-data provenance

Every market history on this site comes from one of three sources published for research, and from nowhere else. Each is fetched on the operator's administration site, checked against the version already shown, and only then published to the site's own database; no page fetches market data while you are using it. The series are whole markets, not the funds or the branded indices you would buy.

Robert J. Shiller, Online Data

Robert J. Shiller, “Irrational Exuberance” data (ie_data.xls), shillerdata.com. Converted to euro with the Federal Reserve H.10 rate (1971–1998, via FRED EXGEUS at the fixed 1.95583) and the ECB reference rate (from 1999).
Terms: Published freely by Robert J. Shiller for research and teaching; shown here with attribution. Licence

Kenneth R. French Data Library

Eugene F. Fama and Kenneth R. French, Data Library, market factor plus risk-free rate, Dartmouth College. Converted to euro with the ECB reference rate.
Terms: Copyright Eugene F. Fama and Kenneth R. French, published freely for research; shown here with attribution. Licence

Jordà-Schularick-Taylor Macrohistory Database

Òscar Jordà, Moritz Schularick, and Alan M. Taylor. 2017. “Macrofinancial History and the New Business Cycle Facts.” in NBER Macroeconomics Annual 2016, volume 31, edited by Martin Eichenbaum and Jonathan A. Parker. Chicago: University of Chicago Press. Data: JST Macrohistory Database, Release 6, macrohistory.net.
Terms: Creative Commons Attribution-NonCommercial-ShareAlike 4.0: non-commercial use, with attribution, and anything derived from it shared under the same licence. Licence

European Central Bank, reference exchange rates

ECB reference exchange rate, US dollar/Euro: monthly average (EXR.M.USD.EUR.SP00.A) and end of month (EXR.M.USD.EUR.SP00.E).
Terms: Reusable with the source named, for any purpose.

The ETF-or-property comparison replays German prices beside these: house prices from the Bank for International Settlements, flat prices and asking rents for cities from GREIX, the German Real Estate Index of the Kiel Institute, consumer prices from the Federal Statistical Office (Destatis), and mortgage rates from the Deutsche Bundesbank. They are read once a year into the site's code, and the comparison names each one under its result.

Two of these sources allow non-commercial use only. This site is free, carries no advertising and sells nothing, which is the condition it shows them under.

Source and review standard

Primary law, ministries, regulators, courts, pension authorities, central banks and index providers establish the rule or data definition. Third-party calculators are used only as independent numerical checks and never override a primary source.

This register lists the calculation version, scope, review dates and original sources for each calculator and guide. The shared footer links here from every page.

How we work

Who writes

One person writes the calculators, the guides and the arithmetic behind them. There is no editorial team and no ghost-writing for anyone else. A page states when it was last checked and against which sources.

Where the figures come from

Every statutory figure – a tariff, a ceiling, a rate, an allowance – is kept in one register with the law it comes from and the date from which it applies. A page never types a figure of its own; it reads the register, and an automated check fails if a sentence and the register disagree.

The calculators are checked against answers from outside this site: the wage tax against the Federal Finance Ministry's own program, contributions against the published tables. A calculation without such an outside check is said to be an estimate, or written as a guide instead of a calculator.

When figures are updated

Once a year, on a fixed checklist: in January the income-tax tariff, the contribution ceilings, the Basiszins and the health and care rates a pensioner pays. An e-mail reminder goes out before each is due. Anything else is updated when the law that sets it changes. Each update is checked against its official source and dated on the pages it affects.

When something is wrong

Write to us if a figure looks wrong; please include the page and the inputs you used. A confirmed error is fixed, and if the fix changes a result, the change is listed below with its date and a new calculation version. A link saved before the change still opens the old calculation, with a notice saying what has changed since.

Independence and funding

The site is paid for privately. It has no advertising, no affiliate links, no sponsors and no paid placements, and it does not name, rank or recommend products, banks, brokers or insurers. Nobody outside the project has seen or approved a page before publication.

Outside review

The German rules have not yet been reviewed by a tax adviser or pension consultant. When they are, each page will name the reviewer and the date of the review in its evidence box, and the review will be repeated every year.

When an answer last changed

Three dates about a calculator get confused with each other, so this page keeps them apart. A review can pass with nothing changing. A source date is the day a page was read. This is the third one: the reason a figure you saved might not match the figure you get today.

The register starts where the evidence starts, not at the beginning of the project. Earlier releases recorded what changed in prose and in commits, but never mapped a change to the pages whose answer it moved, and reconstructing that now would be a reading of the history rather than a record of it. A page with nothing listed here says so beside its sources instead of pointing at a history that was never published.

Each entry links to the part of this page explaining how the calculation works now, so the change can be read rather than taken on trust. Each is also recorded against a file in the source this site is built from; that reference is kept for whoever maintains it, and is not published here because a filename you cannot open is not evidence. A change from here on is recorded as it is made.

What it deliberately does not model

The most useful section on this page.

• Costs. Ongoing costs are one yearly percentage, the TER plus any custody fee, taken from the portfolio a twelfth at a time; or leave it at 0 and enter a return that is already after them. Historical fund prices already have the fund's own costs deducted. Order fees and bid-ask spreads are not modelled.
• Sequence-of-returns risk, except in Monte Carlo and historical mode. A fixed rate assumes returns arrive smoothly, which is precisely the assumption that flatters a retirement drawdown – a bad first decade of retirement does far more damage than the same decade later.
• Your pension entitlement. A pension is an amount you enter and the plan schedules, not one it works out for you. It does not know your Entgeltpunkte, your Zugangsfaktor or the tax on your pension. What it does with the figure you give it is set out below.
• Your actual tax position. One effective rate and one allowance are applied to realised gains, and the allowance is assumed to be entirely available to this plan. The model does not know your other income, your marital status, or how much of the allowance your bank has already used on a different account.
• Distributing funds. The Vorabpauschale is modelled for an accumulating fund only. A distribution would reduce the charge and be taxed on its own, and neither is guessed for you – switch the charge off if your fund pays out.
• Life. The plan runs exactly as entered, for as long as entered. No contribution gaps, job changes, illness or divorce.

None of this makes a projection useless. It makes it an estimate of one scenario under stated assumptions, which is all any projection has ever been.

What a pension in a projection actually is

This page said for a long time that no pension of any kind was included. That stopped being true when the engine gained a pension schedule, and the real limit is a narrower one.

What you enter

A monthly amount in today's money, and the month it starts. Further steps can be added, so a small occupational pension arriving before the state pension is two entries rather than an average of the two.

How it is treated

As income you receive, net of whatever tax it attracts. It never enters or leaves the portfolio, so it is never sold and never taxed as a capital gain. It rises with inflation by default; a real increase or decrease on top of that is a separate input.

What it does to the portfolio

Nothing. It is added to the portfolio withdrawal, not netted off it: a plan drawing 1,000 a month from the portfolio alongside an 800 pension has 1,800 of income, and the portfolio is drawn down exactly as fast as it would be without the pension. To model a pension that covers part of a target, lower the portfolio withdrawal yourself by the amount the pension supplies.

What it does not do

It does not derive your entitlement, apply a Zugangsfaktor, or work out the tax on it. Enter what you expect to receive after tax.

If you do not know what to enter, take the monthly amount from your own Renteninformation letter. The Deutsche Rentenversicherung sends one each year from age 27 and answers questions about it.

Privacy, in one line

The public simulator stores nothing you enter: figures are sent to the server, used to compute a result in memory, and not written down. The full account is in the Datenschutzerklärung.

Not advice

This is an educational tool. It is not investment, legal or tax advice, and it is not a recommendation to buy or sell anything. Past performance does not predict future returns. For a decision that matters, talk to someone qualified who knows your situation.