Compound interest means earning interest on your interest, not just on what you put in — the gap between simple growth and compound growth widens every year, which is why time is the most powerful variable in the calculation.
A £10,000 investment at 5% per year earns £500 in year one. In year two it earns interest on £10,500, giving £525. That extra £25 didn't come from you — it came from interest earning interest on itself. Over a short period this looks like a small difference; over 20 or 30 years it becomes the majority of the final balance. Albert Einstein may or may not have called it the eighth wonder of the world, but the maths is unambiguous.
The same annual rate compounds to a higher total when applied monthly rather than annually, because each month's interest starts earning sooner. Daily compounding adds a little more still, though the difference between monthly and daily is small compared to the difference between annual and monthly. For savings accounts and ISAs, monthly compounding is typical. For some bonds and fixed-term deposits, annual compounding is the norm — always check the account terms rather than assuming.
Adding a monthly contribution on top of a starting lump sum accelerates growth further, because every contribution starts compounding from the moment it's added rather than waiting until the end of the term. This calculator spreads your monthly contribution evenly across each compounding period and adds interest on top, then shows the running split between what you contributed and what interest actually earned in the year-by-year table below.
This calculator assumes a fixed interest rate for the entire term, no fees, and no tax — real investments (stocks, funds) don't grow at a steady rate, and interest on savings may be taxable outside a tax-advantaged wrapper like an ISA. Treat the result as an illustration of how compounding works, not a guaranteed return.