Compound Interest Calculator

Why compounding looks unremarkable and then does not

Compound interest is interest earned on interest. In year one it is indistinguishable from simple interest. In year thirty it dominates everything else in the calculation, and that non-linearity is why the concept is so consistently underestimated.

£10,000 at 7% earns £700 in the first year. In year twenty it is earning around £2,500 a year on the same original stake, because it is now compounding on roughly £36,000. Nothing changed except time.

The Rule of 72 is a useful shortcut: divide 72 by the annual return to get the approximate doubling time. At 7%, money doubles about every ten years. At 3% it takes twenty-four. The gap between those two rates is the difference between four doublings and one over forty years.

Time matters more than amount

The single most important variable is how long the money compounds, and it is the one people control least well because it is decided by when they start.

Consider two savers. One invests £200 a month from 25 to 35, then stops and never adds another penny. The other starts at 35 and invests £200 a month until 65. At 7%, the first — who contributed £24,000 over ten years — ends up with roughly as much as the second, who contributed £72,000 over thirty. The first saver's money simply had longer to compound.

This is why the standard advice is to start with whatever you can rather than waiting until you can afford a meaningful amount. The early years contribute disproportionately, and they are not recoverable later.

Compounding frequency, and why it barely matters

Compounding monthly rather than annually does help, but far less than most people assume. At 10% for one year, annual compounding gives 10.00%, monthly gives 10.47%, and daily gives 10.52%. The difference between monthly and daily is five hundredths of a percent.

The mathematics has a ceiling: as frequency increases the result approaches a limit of e^r − 1, so there is a hard maximum no amount of extra compounding can exceed. Do not choose one savings product over another for its compounding frequency alone; the headline rate matters vastly more.

Where frequency does matter is in comparing quoted rates. A nominal rate compounded monthly is not the same as an annual equivalent rate. Compare APY or AER figures, which already account for compounding, rather than nominal rates.

What this projection ignores

Inflation, most importantly. A projection showing £500,000 in thirty years is in future money. At 2.5% inflation that is worth roughly £238,000 in today's terms. To think in current purchasing power, use a real return — your expected return minus expected inflation — rather than a nominal one.

Tax, which varies enormously by jurisdiction and account type. Returns inside a tax-sheltered account compound on the full amount; returns in a taxable account compound on the after-tax remainder, which over decades is a large difference.

Fees, which are more corrosive than they look. A 1% annual management charge does not reduce your final balance by 1% — it reduces it by roughly 20% over thirty years, because you lose the compounding on every pound of fee as well.

And volatility. This model assumes a steady annual return. Real markets do not deliver that, and the order in which good and bad years arrive matters a great deal when you are drawing money out.