The concept that makes patient investors rich. Explained simply, with worked examples.
Compound interest means earning interest on your interest. Once your investment earns a return, that return is added to your principal, and next year you earn a return on the bigger total. The year after that, bigger still. Over time, this snowball effect becomes dramatic.
The alternative — simple interest — is earning interest only on your original principal, with the interest paid out and not reinvested. Simple interest grows linearly. Compound interest grows exponentially. The difference is enormous over long periods.
You invest £10,000 at 7% per year for 30 years.
Simple interest: £10,000 × 7% = £700/year. After 30 years: £10,000 + (£700 × 30) = £31,000.
Compound interest: The formula is A = P × (1 + r)^n, where P is the principal (£10,000), r is the annual rate (0.07), and n is the number of years (30).
£10,000 × (1.07)^30 = £10,000 × 7.612 = £76,123.
That's more than double the simple interest result, from the same initial investment, the same rate, and the same timeframe. The difference — £45,000 — was created by interest compounding on itself over 30 years.
There's a quick mental trick for estimating how long it takes an investment to double: divide 72 by the annual interest rate. The result is the approximate number of years to double.
If you invest £20,000 at 7% and leave it, it becomes £40,000 in about 10 years. Then £80,000 in 20 years. Then £160,000 in 30 years. The growth accelerates in the later years — the last decade generates more than the first two decades combined.
This is the most important practical implication of compound interest, and it runs counter to how most people think about saving.
Investor A starts at age 25, contributes £200/month until age 35, then stops — total contributions £24,000. After that, her portfolio just grows untouched until age 65.
Investor B starts at age 35, contributes £200/month every month until age 65 — total contributions £72,000 over 30 years.
Assuming 7% annual return:
Investor A contributed three times less money, didn't contribute for 30 years, and ended up with almost the same pot. The difference was time — Investor A's £24,000 had 40 years to compound; Investor B's £72,000 had an average of 15–16 years.
Start 10 years earlier with the same monthly contributions and you typically end up with roughly twice as much. That's the effect of compound interest over time.
Interest can compound at different frequencies — annually, quarterly, monthly, or daily. More frequent compounding means interest is added to the principal more often, which means you earn interest on interest sooner. The difference matters more at higher rates and longer periods.
On £10,000 at 7% for 20 years:
In savings accounts and ISAs, interest typically compounds monthly. In investment accounts with dividends reinvested, the effective compounding is continuous. For planning purposes, annual compounding is a reasonable approximation.
Compound interest doesn't only apply to savings — it also applies to debt, where it works against you with the same force. Credit card balances at 20–30% interest compound monthly. If you make only minimum payments, the balance can grow for years despite regular payments, because interest is compounding faster than you're paying it down.
On a £3,000 credit card balance at 25% APR, making only minimum payments (say, 2% of the balance), it would take over 25 years to repay and cost over £7,000 in interest. The same compound mechanism, working in the opposite direction.
This is why the financial advice to pay down high-interest debt before investing is generally sound: guaranteeing you don't pay 25% interest is a better return than any investment you're likely to find.
Compound growth looks impressive in nominal terms, but inflation erodes the real value of that growth. If your investment grows at 7% per year and inflation runs at 2.5%, your real return is approximately 4.5%. The doubling time in real terms is 72 ÷ 4.5 = 16 years, not 10.
For long-term planning, always think in terms of real returns. A pension pot of £500,000 in 2050 won't buy what £500,000 buys today — and planning for the right number in real terms is more important than hitting a large nominal figure.
The biggest mistake is waiting to start. People tell themselves they'll invest "once things settle down," or "when they have more to put in," or "after the next raise." Time lost in the early stages of compounding is extraordinarily costly — far more costly than a smaller contribution started early.
A second common mistake is interrupting the compounding — selling investments during market downturns, withdrawing money for non-emergencies, or switching into cash at the wrong time. Compounding requires time and consistency to work. Taking money out resets the clock on the portion you withdrew.
Start small if that's what's possible. £50/month at 25 compounds into far more than £200/month at 40. The amount matters less than the start date.