Albert Einstein may or may not have called compound interest the eighth wonder of the world — historians argue about whether he actually said it. But the mathematics behind the idea is genuinely extraordinary, and it's one of the few financial concepts where understanding it even slightly changes what you do with money.
Simple interest is linear. You put £1,000 in an account at 5% per year, you earn £50 every single year. After 10 years you have £1,500. The growth is predictable, flat, and honestly a bit dull.
Compound interest is different. You earn interest on your interest. In year one you earn £50. In year two, you earn 5% on £1,050 — that's £52.50. In year three, 5% on £1,102.50. The base keeps growing. The interest payments keep growing. Over time the curve stops looking linear and starts looking exponential.
After 10 years of compounding at 5%, that £1,000 becomes £1,629 — not £1,500. After 20 years, £2,653. After 40 years, £7,040. The extra £5,500 over 40 years came from doing absolutely nothing except not touching it.
There's a shortcut for working out how long it takes your money to double: divide 72 by your annual return rate.
The S&P 500 has returned around 10% annually on average over the past century, including dividends. At that rate, a portfolio doubles roughly every 7 years. Start at 18 with £5,000 and leave it alone: by 25 you have £10,000, by 32 you have £20,000, by 39 you have £40,000, by 46 you have £80,000, by 53 you have £160,000, by 60 you have £320,000. Starting with £5,000. Doing nothing.
The Rule of 72 works in reverse too. Inflation of 3% halves your purchasing power in 72 ÷ 3 = 24 years. Credit card debt at 25% APR doubles what you owe in about 3 years if you only make minimum payments. Compound interest is a weapon — it works for you in investments and against you in debt.
This is where it gets genuinely unfair in your favour as a young investor. Three people, all investing in a fund returning 8% per year:
| Investor | Starts | Monthly amount | Stops investing | Total put in | Value at 65 |
|---|---|---|---|---|---|
| Alex | Age 18 | £50/month | Age 27 | £5,400 | £169,000 |
| Blake | Age 27 | £50/month | Age 65 | £22,800 | £161,000 |
| Sam | Age 35 | £200/month | Age 65 | £72,000 | £272,000 |
Alex invested for just 9 years and then stopped entirely. Blake invested for 38 years straight, putting in over four times as much. Yet their outcomes at 65 are almost identical. Alex put in £5,400. Blake put in £22,800. The single variable that explains it: Alex started 9 years earlier.
Sam invested £200 a month for 30 years — £72,000 total — and ends up ahead of both. But Sam needed to invest 13× more than Alex to get there, because Sam started 17 years later.
In a savings account, compounding is straightforward — interest is added to the balance each year. In the stock market it works through two mechanisms:
Dividend reinvestment: when a company pays dividends and you reinvest them to buy more shares, those new shares also pay dividends. Your share count grows over time, and so does the dividend income generated. This is the mechanical basis of a DRIP (Dividend Reinvestment Plan) and it compounds remarkably over decades.
Price appreciation on a growing base: if your portfolio rises 10% this year, next year's 10% is calculated on a larger number. A portfolio worth £10,000 that returns 10% is worth £11,000. Next year's 10% return on £11,000 is £1,100 — more than the year before, despite the same return rate. The absolute gains get larger every year even when the percentage stays constant.
Warren Buffett made roughly 99% of his net worth after his 50th birthday. Not because he suddenly became a better investor — he'd been exceptional since his teens. But because compound interest works slowly for decades and then explosively at the end. He started at 11 and had 39 years of compounding before turning 50. The snowball got enormous. By the time it was rolling fast, it was already huge.
This is the part most people miss. A fund charging 1.2% per year versus one charging 0.1% sounds trivial. Over 30 years, on a £50,000 portfolio growing at 8%, the 1.2% fee fund leaves you with around £390,000. The 0.1% fee fund leaves you with around £490,000. The difference — £100,000 — went to the fund manager. Not because they earned higher returns, but because their fee compounded against you at the same rate your returns were compounding for you.
Taxes work the same way. Every time you sell an investment outside an ISA and pay capital gains tax, you're removing money from the compounding base. £2,000 paid in CGT today, at 8% compounding, would have been worth £9,850 in 20 years. ISAs eliminate this drag entirely — which is a large part of why they're so valuable over long time horizons.
A = P × (1 + r/n)nt
Where A = final amount, P = principal (what you start with), r = annual interest rate as a decimal, n = how many times interest compounds per year, t = years. For most long-term investing purposes, annual compounding (n=1) is close enough for back-of-envelope calculations.
The one thing to take from this lesson: time is the most powerful input in the compound interest formula — more powerful than the rate and more powerful than the amount you invest. Every year you delay starting is a year of compounding permanently lost. Not delayed — lost. The money you could have invested at 18 and didn't will never compound from 18. That's the real cost of waiting.
The Rule of 72 is a shortcut for estimating how long an investment takes to double: divide 72 by your annual return rate. At 8% a year, 72 ÷ 8 = 9 years to double.
It depends on the rate. At 6% money doubles in about 12 years, at 8% in about 9 years, and at 10% in roughly 7 years — the Rule of 72 gives you the estimate instantly.
Because compounding accelerates over time. The earliest money you invest has the most years to grow, so a teenager investing small amounts can end up ahead of someone who starts later with far larger sums.
Want the full picture? Read our guide on how to invest as a teenager in the UK.
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