Compound interest: the formula and its limits
Compounding means that the result of one period becomes part of the starting amount for the next. It describes a calculation, not a promise that an investment will earn a positive return.
Translation draft — pending human editorial review.
Start with the assumptions
For an initial amount C, a rate r per period and n periods, the theoretical balance is C × (1 + r)^n. This assumes a constant rate, no withdrawals and no additional contributions. The rate and the time unit must match: an annual rate cannot be used as a monthly rate.
A model is not a forecast
A calculator applies the assumptions you enter. A displayed balance does not show that the assumed rate will be available, or that you can maintain it for the whole period.
Follow the money through three years
With an illustrative €1,000 and a 5% annual rate, the first year ends at €1,050. The second ends at €1,102.50. The third ends at €1,157.63 after rounding. The 5% rate is used only to explain the arithmetic.
Compare with simple interest
If the annual €50 were always calculated on the original €1,000, the three-year total would be €1,150. The €7.63 difference comes from earning a result on earlier results.
Include losses and costs
A 10% rise followed by a 10% fall does not restore the original balance. €1,000 becomes €1,100 and then €990. The percentages apply to different starting amounts. Fees, taxes and withdrawals can also reduce the amount carried forward.
Change one assumption at a time
Compare scenarios with the same starting amount, contributions and period. Then change the rate or costs to see what drives the result. For a goal with a deadline, keep the contributions you control separate from returns you cannot control.
Frequently asked questions
Does compounding guarantee growth?
No. Negative returns can reduce the amount carried into the next period.
Is an average return enough?
Not always. The sequence of returns, contributions and withdrawals can affect the outcome.
Conclusion
Use compounding to understand a relationship between time, money and returns. Keep the assumptions beside the result and avoid treating a scenario as an investment promise.