Compound interest is interest earned on interest already earned. Because each period’s growth becomes part of the base for the next, the balance grows exponentially rather than linearly.
Time matters more than rate
The exponent is where the leverage sits. £1,000 at 7% becomes £1,967 after ten years, £3,870 after twenty and £7,612 after thirty. Each additional decade adds more than the last, which is why starting early outweighs almost any other decision in long-horizon saving.
The rule of 72
Divide 72 by the annual percentage rate for a close approximation of the doubling time. At 6%, money doubles in about twelve years; at 9%, in eight. It is accurate to within a few percent for rates between roughly 4 and 15.
Compounding frequency
More frequent compounding gives slightly more, with diminishing returns. At a 10% nominal rate, yearly compounding yields 10.00%, monthly 10.47%, and continuous compounding 10.52% — the ceiling. Always compare effective annual rates rather than nominal ones.
Inflation and fees
A 7% return with 3% inflation is roughly 4% in real terms, and the same exponential arithmetic works against you. A 1% annual fee on a portfolio compounding at 7% for thirty years consumes roughly a quarter of the final balance. This calculator shows nominal figures only.
These are arithmetic projections, not predictions. Actual returns vary, and nothing here is financial advice — for decisions that matter, talk to a qualified adviser.