How compound interest works its magic on investments

Illustration of compound interest – a man standing on stack of gold coins with a clock showing time passing.

(Image credit: Getty Images)

published 25 October 2023

Start investing as early as you can to ensure you benefit from the magic of compounding, says Dominic Frisby.

Speculating in small stocks is one answer – the problem is that you risk losing your shirt. But there is another, safer option. All you need is time (lots of it) and some discipline.

You will often hear it said that time in the market is more important than timing the market. There is a lot of wisdom to the adage, although, in defence of timing, get it right and you gain a significant advantage. The underlying wisdom derives from the power of compounding, which Albert Einstein called the eighth wonder of the world. “He who understands it, earns it. He who doesn’t, pays it,” he is supposed to have said. (It is one of those attributed quotes, but it’s better coming from Einstein than anyone else, I suppose.)

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How does compound interest work?

If I offered you one million pounds up front, or a magic penny that doubles in value every day for 30 days, would you take the million? I imagine you would. Big mistake! A penny that doubled every day would be worth more than £5m on day 30.

But here’s the thing: it is the effect of compounding in the later stages that is breathtaking. The early stages are muted. Take that magic penny. On day ten, it’s only worth a fiver. By day 20 it’s north of five grand. But it’s in the last three or four days that the vast sums are made.

Compounding works even for relatively low annual returns. To benefit from it you have to start as early as you possibly can, reinvest everything you make and, ideally, keep adding. But it enables you to turn small sums into large ones. Just ask Warren Buffett.

The table below shows the effects of compounding at different rates of return over 40 years but assumes you don’t add to the initial pot. If you do, the effects are more dramatic. Tell your children about compounding, and get them saving and investing. They’ll thank you.

Swipe to scroll horizontally

Compound interest at different rates of return
Period	5%	7%	10%	16%	20%
1	£1.05	£1.07	£1.10	£1.16	£1.20
2	£1.10	£1.14	£1.21	£1.35	£1.44
3	£1.16	£1.23	£1.33	£1.56	£1.73
4	£1.22	£1.31	£1.46	£1.81	£2.07
5	£1.28	£1.40	£1.61	£2.10	£2.49
6	£1.34	£1.50	£1.77	£2.44	£2.99
7	£1.41	£1.61	£1.95	£2.83	£3.58
8	£1.48	£1.72	£2.14	£3.28	£4.30
9	£1.55	£1.84	£2.36	£3.80	£5.16
10	£1.63	£1.97	£2.59	£4.41	£6.19
11	£1.71	£2.10	£2.85	£5.12	£7.43
12	£1.80	£2.25	£3.14	£5.94	£8.92
13	£1.89	£2.41	£3.45	£6.89	£10.70
14	£1.98	£2.58	£3.80	£7.99	£12.84
15	£2.08	£2.76	£4.18	£9.27	£15.41
20	£2.65	£3.87	£6.73	£19.46	£38.34
25	£3.39	£5.43	£10.83	£40.87	£95.40
30	£4.32	£7.61	£17.45	£85.85	£237.38
35	£5.52	£10.68	£28.10	£180.31	£590.67
40	£7.04	£14.97	£45.26	£378.72	£1,469.77

To maximise the benefit of compounding, you also need to keep fees and taxes to a minimum, to ensure that as much money as possible gets reinvested. Avoid losses like the plague. Keep adding to the pot, and the compounding works even more in your favour.

There is an excellent tool on Monevator that allows you to see the effects.

An initial deposit of £5,000, with £2,000 added every year and a 7% rate of return, becomes half a million in 40 years and a million in 50. Invest just £2,150 every year at 7% and in 50 years you will have a million.
But at the same rate over a 15-year period, you would have to invest £33,800 –15 times as much – to get to a million.

The rule of 72

There is also a useful predictive tool that can tell you how long it will take for your money to double, assuming you compound at a certain rate. It’s called the rule of 72.

Divide 72 by your annual rate of return and that will tell you the number of years it will take your portfolio to double. Put in mathematical terms, 72 ÷ rate of interest/return = number of years.

Let’s say you have a 5% annual rate of return: 72 divided by five is 14.4, so that’s how long it will take for your money to double: 14 years, five months, give or take. At 10% you will double your money every seven years. All this is before inflation, which is not taken into account in compounding calculations.

You can also use the rule of 72 to see how long it will take for your money’s purchasing power to halve. Say inflation is 8%: divide 72 by eight and the answer is nine. So at 8% inflation, your money will lose half its value in just under a decade. At the suppressed interest rates of the 2008 to 2021 period, compounding is a very different matter. Savings left in cash at 0.1% would take 720 years to double.

Of course, if you lose money, in a given year, it’s a very different story. Compound purists avoid losses like the plague, as we all should, and most of the time steer clear of cyclical sectors that can be prone to prolonged bear markets unless they feel they can time them. That’s why compounding works well in conjunction with a diversified portfolio.

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Dominic Frisby (“mercurially witty” – the Spectator) is the world’s only financial writer and comedian. He is MoneyWeek’s main commentator on gold, commodities, currencies and cryptocurrencies. He is the author of the books Bitcoin: the Future of Money? and Life After The State. He also co-wrote the documentary Four Horsemen, and presents the chat show, Stuff That Interests Me.

His show 2016 Let’s Talk About Tax was a huge hit at the Edinburgh Festival and Penguin Random House have since commissioned him to write a book on the subject – Daylight Robbery – the past, present and future of tax will be published later this year. His 2018 Edinburgh Festival show, Dominic Frisby's Financial Gameshow, won rave reviews. Dominic was educated at St Paul's School, Manchester University and the Webber-Douglas Academy Of Dramatic Art.

You can follow him on Twitter @dominicfrisby