Compound Interest, Explained With Real Numbers
How compounding frequency and time horizon change your final balance, with worked examples.
Compound interest is the reason a modest, boring monthly contribution beats an occasional large one, and the reason a credit-card balance behaves so differently from a personal loan. The mechanic is simple; the consequences take decades to show and are almost impossible to intuit.
The formula and what each term does
A = P × (1 + r/n)^(n×t)
P = starting principal r = annual rate (decimal)
n = compounds per year t = years
A = final amountWith regular contributions the future value of the deposits is added on top:
FV = PMT × [((1 + i)^N − 1) / i] i = r/n, N = n×tA concrete example
£5,000 invested at 7% for 25 years, compounded monthly, becomes about £28,600. Add £200 a month and the total reaches roughly £190,000 — of which around £65,000 is your own money and the rest is growth on growth.
| Years | Balance (lump sum only) | Balance (+£200/month) |
|---|---|---|
| 5 | £7,090 | £21,400 |
| 10 | £10,050 | £45,000 |
| 20 | £20,200 | £117,900 |
| 25 | £28,600 | £190,300 |
Compounding frequency
More frequent compounding pays slightly more, with rapidly diminishing returns. On £10,000 at 6% for one year:
| Frequency | Effective yield | Balance after 1 year |
|---|---|---|
| Annual | 6.00% | £10,600.00 |
| Quarterly | 6.14% | £10,613.64 |
| Monthly | 6.17% | £10,616.78 |
| Daily | 6.18% | £10,618.31 |
This is why advertised rates should always be compared as APY (or AER), not as the headline nominal rate — the APY calculator converts between them.
The rule of 72, and when it breaks
Dividing 72 by the rate approximates the doubling time: at 8%, money doubles in about nine years. The shortcut is accurate between roughly 4% and 12% and drifts badly outside that range, where you should use the exact logarithm instead.
exact doubling time = ln(2) / ln(1 + r)Compounding works against you too
Credit-card debt compounds daily. A £3,000 balance at 22% APR, with only the 2% minimum payment made each month, takes over 20 years to clear and costs more in interest than the original balance.
Inflation and fees quietly shrink the curve
Real return is what remains after inflation and charges. A 7% nominal return with 3% inflation and a 1% platform fee is a real return near 3%, which roughly halves the 25-year outcome. Both belong in any projection you take seriously.
- Compare funds on total cost, not headline performance.
- Model at least one scenario with lower returns and higher inflation.
- Reinvest dividends: excluding them removes most of the compounding effect from equity returns.
Run scenarios with the compound interest calculator, then sanity-check purchasing power using the inflation calculator.
Frequently asked questions
What is the difference between APR and APY?
APR is the nominal annual rate ignoring compounding within the year; APY (or AER) includes it. For any product compounding more often than annually, APY is the higher and more honest figure.
Is it better to invest a lump sum or drip-feed it?
Historically, investing a lump sum immediately wins about two-thirds of the time because markets rise more often than they fall. Drip-feeding reduces the regret risk of a badly timed entry, which is a behavioural benefit rather than a mathematical one.
Does compounding apply to savings accounts?
Yes, but the rate usually trails inflation, so a savings balance can compound in pounds while shrinking in purchasing power. Savings accounts are for stability and short horizons, not growth.
How much difference does one percentage point make?
Over 30 years, 6% versus 7% on £10,000 is roughly £57,400 against £76,100 — about a third more, from a single point.