Compound Interest, Explained With Numbers

Compound interest means interest is calculated on interest you've already earned, not only on the money you originally put in. Said that way it sounds like it should produce fast, dramatic growth from day one. In practice it does the opposite for a long time — the effect is genuinely slow at first, and that is not a flaw in the maths, it's the entire mechanism.

The formula

FV = P(1 + r/n)^(nt) + C × [ ((1 + r/n)^(nt) − 1) ÷ (r/n) ]

The first term grows the starting balance P on its own. The second grows a stream of regular contributions C, each of which compounds for however many periods remain after it's paid in — a contribution made in year one compounds for nearly the whole period; one made in the final year barely compounds at all. That asymmetry is why the timing of contributions matters, not just their total.

Worked example: £5,000 start, £200/month, 6% for 20 years

Final balance: £108,959. Of that, £53,000 (the £5,000 start plus 240 × £200) is money actually paid in, and £55,959 is growth.

Growth's share of the balance doesn't cross half until the very end of the twenty-year run. For most of the period, the balance is mostly a record of what you paid in — the compounding is happening, but on a base too small for it to be visually dramatic yet. That is the honest shape of the curve, and it's worth seeing plainly rather than through a marketing chart that starts the axis somewhere flattering.

Why starting early matters more than the early years suggest

The reason to start early isn't that the early years themselves produce much growth — they visibly don't, per the table above. It's that the early years are what create the base the later years compound on. A pound contributed in year one has been compounding for nineteen years by the time the twentieth year's growth is calculated; a pound contributed in year nineteen has had almost none. Delaying the start by five years doesn't just remove five years of contributions — it removes the base that the following fifteen years would have compounded on top of.

Does compounding frequency matter much?

Less than most people expect, at typical savings rates. Moving from annual to monthly compounding at 6% increases the effective annual rate from 6.00% to about 6.17% — a real difference, but a modest one compared to the effect of the rate itself or of the contribution size. Frequency matters far more at high rates over long periods than at the rates and periods most personal saving involves.

Why the final figure isn't today's buying power

£108,959 in twenty years does not buy what £108,959 buys today — the calculation above is nominal, meaning it doesn't subtract inflation. To get a rough sense of real purchasing power, use an expected-return figure that is already net of expected inflation (a real rate) rather than the nominal rate a savings or investment product quotes.

Common mistakes

• Assuming a constant rate of return. Real investment returns vary year to year and can be negative in any given year — the formula above is a projection under a fixed assumption, not a forecast.
• Forgetting fees. Platform fees and fund charges compound too, working against the balance the same way interest works for it.
• Ignoring tax on interest, dividends or gains, which reduces the figure actually available to spend.
• Reading the headline final figure and skipping the contributions-vs-growth breakdown, which is what actually explains whether the projection is doing anything unusual.

Limitations

• A projection under fixed assumptions, not a forecast — past performance does not indicate future returns.
• Contributions are assumed to be made at the same amount, at the end of each period, throughout — real contribution patterns are rarely that regular.
• This is a calculation, not regulated investment advice.