Understanding ETFs, savings plans and compound interest

Four tools for the most important money questions

Private finance questions usually revolve around four topics: saving, interest, loans and inflation. For each topic the portal provides a dedicated tool:

Compound interest: why time is decisive

The classic compound-interest formula reads:

• End capital = starting capital × (1 + interest rate)^term

The strength sits in the exponent. Investing 10,000 € at 5 % per year for 30 years yields:

At 7 % per year, the end capital after 30 years would be about 76,123 €. A seemingly small difference in interest rate becomes almost double the end amount – the effect of exponential growth.

A useful rule of thumb is the rule of 72: 72 ÷ interest rate ≈ doubling time in years. At 6 %, capital doubles roughly every 12 years; at 4 % every 18 years.

Important caveat: compound interest always holds mathematically. Whether it materialises depends on whether interest can be received safely and reinvested. For equities and ETFs, returns are not constant; the formula describes an average that fluctuates strongly over short horizons.

ETF savings plan: regular contributions instead of one lump sum

In an ETF savings plan you invest a fixed monthly amount in a broadly diversified index, for example the MSCI World or the FTSE All-World. Over long horizons, broadly diversified equity ETFs have historically delivered an average real return of 5 to 7 % per year after inflation – with significant swings in individual years.

The mechanics in short:

1. The monthly contribution is invested automatically
2. Shares are bought at the current price – at low prices, more shares per euro
3. Distributions or accumulations add to the assets
4. Over long horizons, swings tend to even out

A worked example with 200 € per month over 30 years at an assumed 6 % per year:

Only about 36 % of the end capital is your contributions – the rest is appreciation. This is the compound-interest effect in the savings-plan context. The ETF savings-plan calculator shows this logic in transparent yearly steps.

Costs: the TER is the silent brake

Every ETF has running costs, expressed as the Total Expense Ratio (TER). Over long horizons the TER has a clear impact, because it acts like a negative compound interest that eats into returns. A comparison over 30 years, 200 € monthly, 6 % before costs:

The gap between 0.07 % and 1.50 % TER over 30 years is around 43,000 € in end value. That is why checking the TER before opening a savings plan pays off. The ETF calculator includes the TER explicitly.

Loan arithmetic: annuity, interest share, outstanding balance

A classic annuity loan has a constant monthly payment. The formula:

• Annuity = principal × (i × (1 + i)^n) ÷ ((1 + i)^n − 1)

with i = monthly interest rate (annual ÷ 12), n = number of months.

An example: 200,000 € principal, 3.5 % effective annual rate, 20-year term (240 months). The monthly payment is about 1,160 €. The split between interest and principal shifts over time:

The total of all payments is about 278,400 €. Of that, 200,000 € is principal and 78,400 € is interest – almost 40 % above the original loan. This is normal for long terms and shows the price of time.

Special repayments are particularly effective in the early years because they lower the outstanding balance and thus future interest. 5,000 € special repayment in year 2 saves significantly more interest over the full term than the same 5,000 € in year 18.

The car-loan calculator shows monthly payment, interest share and outstanding balance transparently for a classic annuity loan. When comparing offers, always use the effective annual rate – it includes the main loan fees and is uniformly defined under the German Price Information Regulation (PAngV).

Inflation and real return

Inflation is the annual change in the consumer price index. It acts like a "negative compound interest" on the purchasing power of money not invested. At 3 % inflation per year, cash loses value:

After 20 years only a little over half remains in real terms – even though the nominal amount is unchanged.

The real return subtracts inflation from the nominal return:

• Real return ≈ nominal return − inflation rate (simple)
• Real return exactly = (1 + nominal) ÷ (1 + inflation) − 1 (Fisher formula)

A 4 % fixed deposit at 3 % inflation yields only about 1 % of real purchasing-power growth – significantly less than the nominal number suggests.

The ETF calculator can incorporate an inflation assumption and report the inflation-adjusted end capital.

Capital gains tax

In Germany capital gains are taxed at a 25 % flat tax, plus a 5.5 % solidarity surcharge on top of that, and possibly 8 % or 9 % church tax. The total burden is around 26.375 % (without church tax) or 27.82–27.99 % (with church tax).

The saver's allowance of 1,000 € (single) or 2,000 € (jointly assessed) is tax-free. With a Freistellungsauftrag at the bank, the allowance is used up before tax is withheld.

For accumulating equity ETFs, the annual lump-sum advance taxation (Vorabpauschale) also applies. If price appreciation is high enough, a fictional minimum amount is taxed each year. This tax is offset against tax at sale, so there is no double taxation in the end – only a cash-flow effect.

Diversification and risk

Mathematical returns say nothing about risk. The historical swings of broad equity ETFs are on the order of ±20 to ±35 % in single years. Over 10–15 years these swings have historically smoothed out, but no one guarantees this for the future.

Risk reduction mainly comes from:

• Broad diversification across many countries and sectors
• Long horizons (at least 10–15 years for equity quotas)
• Avoiding concentration risk (single stocks, single sectors, single countries)
• Conservative assumptions in planning (prefer 4 % over 7 %)

Common errors in financial calculations

• Overly optimistic assumptions: 9 % per year is possible, but risky as a planning base.
• Forgetting inflation: 100,000 € in 30 years are not 100,000 € today.
• Ignoring costs: a TER of 1.5 % instead of 0.15 % eats a six-figure amount over 30 years.
• Under-estimating special repayments: early ones save disproportionately more interest.
• Expecting guarantees where there are none: ETFs have no capital protection – swings are part of the picture.

Conclusion

Finance calculators are useful when they do not promise too much. Compound interest is a real, long-term force, but it is not a guarantee for every individual year. ETF savings plans and conservative return assumptions are planable when you also factor in inflation, costs and taxes. With the four calculators on Ultra-Rechner you see a clean calculation path for each question and can change assumptions immediately.

Sources

• Deutsche Bundesbank – interest rate and inflation statistics – bundesbank.de
• Federal Statistical Office – consumer price index – destatis.de
• PAngV – Price Information Regulation for effective interest rates – gesetze-im-internet.de/pangv_2022
• Income Tax Act, Section 20 – flat tax on capital gains – gesetze-im-internet.de/estg
• BaFin – consumer information on ETFs and investment funds – bafin.de