The next return uses the balance left invested
A 5% return adds €500 to €10,000. Keep that gain invested and the next 5% applies to €10,500. This changing base is compounding.
Hypothetical 5% each year, after ongoing costs and before tax. All returns stay invested; no deposits or withdrawals. A calculation, not a forecast.
- Start€10,000
- After year 1€10,500
→ €10,000 + €500 stay invested for year 2.
- After year 2€11,025
Original capital + €500 retained + €525 new.
Inside the second gain: €525
Upper bars share one euro scale; the second gain is enlarged here.
Spending income removes it from the next base. Market investments combine retained income and price changes; losses shrink the base too.
Calculate the changing base and dated contributions
In year 2, €10,000 × 5% contributes €500 and the retained €500 × 5% contributes €25: €525 in total.
At the same assumed rate, €10,000 becomes €16,289 after ten years or €26,533 after twenty, rounded. Market returns fluctuate and savings rates can change after a fixed term. A 10% loss instead leaves €9,000 for the next return; remaining invested guarantees no recovery.
€100 monthly adds €12,000 over ten years before investment results, potentially much of the growth on a small starting balance. Each contribution has its own starting date: money added in the last month has not been invested for ten years.
Separate initial capital, dated contributions and assumed return in a calculator; investing future contributions on day one overstates their time at work. A precise output makes no rate certain. Test lower returns and affordable funding against ordinary expenses.
A repeated gap accumulates too
A persistent difference in net returns acts on every year’s changing balance. Costs therefore affect more than the current year’s result. Establish what each charge applies to and whether reported returns already include it; chasing a recent winner adds costs without establishing its future return.
Compare 5% and 4% over thirty years
5%€43,219
4%€32,434
Same scale; solid sections are the original €10,000. Rounded ending balances differ by €10,785.
Five to four is one percentage point, or a 20% reduction relative to the 5% rate. It is not a sudden 20% account loss. These after-cost assumptions do not say a particular fee always subtracts exactly one percentage point; balance-based and transaction charges work differently.
Measure what the balance can buy
The balance can grow while each euro buys less. A nominal return measures the money; a real return measures its purchasing power. Divide the balance by the increase in the price of the same basket.
- €10,000Starting balance
- × 1.05 €10,500After a 5% nominal return
- ÷ 1.03 €10,194In starting-year euros, after prices rise 3%
Real return = (1 + nominal return) ÷ (1 + inflation) − 1
1.05 ÷ 1.03 − 1 ≈ 1.94%
One year, no external flows, tax ignored. Both rates refer to the same period, currency and relevant price basket; they are assumptions.
Approximation, price baskets and a future goal
Subtracting gives a useful 2% approximation, not the exact ratio; the difference grows at high rates. A historical UK calculator describes UK prices rather than another country’s basket or the future. A future €30,000 balance may not fund a goal costing €30,000 today: label the price basis of projections.