How the simulation computes

What is computed

One assumed return, applied to every year. Four inputs decide the result, and each of them is explained below in the words that stand behind its info mark on the calculator.

• Annual return. The annual return is the growth rate the calculator applies to every year, unchanged over the whole period. Enter your own assumption or take one of the historical averages from the list below it. The figure is gross, so before product costs, taxes and inflation. What you see in the result is what this one assumption does over the years, not what a market will do.
• Yearly rise of the contribution. Raises the monthly amount by this percentage at the start of every year. The first year is paid at the amount above, the second at that amount plus the percentage. Nought means the same amount for the whole period. At 3 % a year, 100 a month becomes about 180 after twenty years, and that difference is usually larger than the one a slightly better return would make.
• Return variance. The variance is a swing around your return: the best case uses your rate plus the variance every year, the worst case your rate minus it. Set it to what you consider possible, for example three percentage points. The two curves are two fixed assumptions and say nothing about how often such a run occurs. How often an outcome comes up across many simulated runs is what the Monte-Carlo simulation counts.
• Compounding frequency. The compounding frequency says how often interest is credited and starts earning interest itself. Annually means the rate you entered is exactly what the year brings. Monthly brings a little more, because every credit immediately earns as well. It matters for interest products such as a savings account, not for shares or exchange-traded index funds (ETF), whose annual return already contains it. A monthly contribution is always paid in at the start of the month, at the monthly rate that belongs to your interval.

The return assumption

The Simulator and the Beam open on the same values as our Instagram posts: 5,000 to start in every currency, 200 a month and a return of 14.7 % a year. That is the total return of the S&P 500 with dividends, in US dollars, from 2016 to 2025 (cut-off 31 December 2025), as a compound average, before costs, taxes and inflation, worked out from the same series as in the Atlas. Beside the dial it says "S&P 500, last 10 years, no forecast". A single decade can turn out far better or worse than the long run: since 1970 it was 11.0 % a year. US shares with dividends, because there is no free world series. The values are a starting point, not a recommendation.

You can type your own figure or take one of the historical averages below. A figure out of a series is derived from that series and carries its mark. A figure you typed is your own assumption and carries that mark.

• S&P 500: 11.1 % a year, 1971 to 2025. derivedS&P 500, 1971 to 2025
• Gold (USD/oz): 7.7 % a year, 1961 to 2025. derivedGold (USD/oz), 1961 to 2025

Above 15 percent a year the calculator adds a line: A very high return. Averages from short periods cannot be carried forward.

Monte-Carlo simulation

The three lines above are fixed paths: one assumed return each. Monte-Carlo instead runs thousands of random paths from the asset's real year-by-year returns (without a selected asset: random returns around your rate). Read the result like this: in 9 of 10 runs you end above the pessimistic value, in half above the median, in 1 of 10 above the optimistic value. If the pessimistic value is below what you paid in, the plan carries real loss risk over this horizon.

With a series selected, the runs are drawn from the years of that series. Without one, they are drawn around your own rate with the swing you set. Every series is listed under Sources with its publisher and the day it was fetched.

• 2,000 runs.
• Each year drawn independently from the history, so the order of the years is not kept.
• Each year drawn independently around the return you entered, with the swing you set.
• A model, not a forecast.

Around 50 % means typical. Above 90 % means the scenario needs a lot of luck, below 10 % means it is already a bad outcome. Rule of thumb: plan with the base case, check whether you could live with the pessimistic value.

What is left after taxes, costs and inflation

This turns the gross figure into what is left: first product costs as a deduction from the return, then tax on the gain, then inflation. The tax is simplified and taken once at the end of the period, with your annual allowance counted for every year and the partial exemption you entered. Real means the same amount in today's purchasing power, divided by inflation compounded over the years. Every field can be changed. Where the preset values come from is listed under sources.

The preset values per country, as the calculator shows them:

• Germany. Abgeltungsteuer 25 % plus solidarity surcharge (26.375 % together), Sparerpauschbetrag 1,000 € per year, Teilfreistellung 30 % for equity funds. Vorabpauschale and church tax are not included.
• United States. Long-term capital gains at 15 %. Brackets of 0 % and 20 % exist as well. State tax and the 3.8 % net investment income tax (NIIT) are not included. A 401(k) or an individual retirement account (IRA) would change the picture entirely.
• United Kingdom. Capital gains tax 18 % at the basic rate (24 % higher rate), annual exempt amount £3,000. Inside an individual savings account (ISA), gains stay free of tax.
• Euro area, generic. A typical rate of 25 %. Please enter the rate of your own country.
• No taxes. Gross figures, without taxes and without product costs.

Typical values for private investors, official sources, as of tax year 2026, checked monthly and updated automatically when two official sources agree.

Goal calculator

The target is the amount you want to reach at the end of the investment period. Enter an amount and the calculator works backwards: it shows the monthly contribution that would be needed for it, given your initial investment, your return and your period. The figure is before costs and taxes and in future money, not in today's purchasing power. It is an arithmetic quantity at an unchanging return, not a promise.

What every figure is counted in

The line under every result says it in keywords: before costs and taxes · Nominal

• Nominal. An amount counted in the money of the year it falls in, with nothing taken off for rising prices. It is the figure that would be in the account.
• In today's purchasing power. The same amount, converted into what it would buy today at an assumed rate of inflation. It answers what the money is worth rather than what the figure says.
• Price index. An index that follows only the prices of its companies. Dividends paid out along the way are not in it, so its long-run average is below what a holder who reinvested them actually got.
• Total return index. An index that counts the dividends in, as though every payout had been put straight back into the same shares. Over decades that is the larger part of the difference between two indices on the same market.
• before costs and taxes. past returns are not a forecast

Sources, with the day they were fetched

Every line names the publisher, the last year the series covers and the day the figures were last fetched. The full list of every source in the product is on the sources page.

• S&P 500: Aswath Damodaran, NYU Stern. Covers up to 2025, fetched 9 November 2026. Source
• Gold (USD/oz): World Bank. Covers up to 2026-10, fetched 9 November 2026. Source
• What is left after taxes, costs and inflation: Typical values for private investors, official sources, as of tax year 2026, checked monthly and updated automatically when two official sources agree.

All sources