Compound interest
Einstein called it the eighth wonder of the world – find out why.
Most people have heard of the seven wonders of the world. But the eighth might be news to you. Albert Einstein, Ben Franklin and John Maynard Keynes have all been credited with describing compound interest as the eighth wonder of the world.
But for those of you with a curious mind, who need to know all the answers, to save you scratching your head, digging in your memory banks or reaching for the encyclopaedia, here are the original magnificent seven.
The seven wonders of the world
1. The pyramids of Egypt
2. The hanging gardens of Babylon
3. The temple of Artemis at Ephesus
4. The statue of Zeus at Olympia
5. The mausoleum at Halicarnassus
6. The Colossus of Rhodes
7. The Pharos (lighthouse) at Alexandria
It seems that in ancient times the architects have had it all their own way. But for the eighth wonder the men of science and pure thought reclaimed some of the ground.
The greatest mathematical discovery of all time
Einstein once called compound interest "the greatest mathematical discovery of all time". But you don't need a brain the size of a planet to understand compound interest. It’s a fairly simple idea.
Year 1: when you invest money you earn interest. Year 2: you earn interest on both your original investment and the interest from the first year. Year 3: you earn interest on your money and the first two years' interest. And so on. The idea of earning interest on your interest is what makes compound interest such a wonder.
It's a snowball effect. When your money stays invested it grows bigger and bigger, slowly at first but then with increasingly large amounts added to your investment over time. Even if you start with a small amount, given enough time, you can end up with an extremely large sum indeed – provided you don’t spend the interest along the way.
Let’s say you invest £1,000 for 25 years and, for ease of calculation, managed to secure a return of 10%.How much would expect to get back. Simple mathematics would suggest that you might expect to get back £3,500.
(£1,000 x 10% is £100 x 25 years is £2,500 + £1,000 original capital = £3,500)
But in fact, you’d actually do rather better than that. Over three times better. As the chart below shows, from a single investment of £1,000, you’d end up with £10,830.
Year Sum invested Interest End of year value
1 £1,000 £100 £1,100
2 £1,100 £110 £1,210
3 £1,210 £121 £1,331
4 £1,331 £133 £1,464
5 £1,464 £146 £1,611
6 £1,611 £161 £1,772
7 £1,772 £177 £1,949
8 £1,949 £194 £2,144
9 £2,144 £214 £2,358
10 £2,358 £236 £2,594
11 £2,594 £259 £2,853
12 £2,853 £285 £3,138
13 £3,138 £314 £3,452
14 £3,452 £345 £3,797
15 £3,797 £380 £4,177
16 £4,177 £418 £4,595
17 £4,595 £459 £5,054
18 £5,054 £505 £5,560
19 £5,560 £556 £6,116
20 £6,116 £612 £6,727
21 £6,727 £673 £7,400
22 £7,400 £740 £8,140
23 £8,140 £814 £8,954
24 £8,954 £895 £9,850
25 £9,850 £985 £10,830
How to make compound interest work for you
- Save as much as you can for as long as you can
- Stay invested. As the model shows, the value of compound interest really kicks in after 20 years
- Don’t spend the interest. If you had withdrawn interest each year you would only come out with your original investment of £1,000!
Of course, trying to work out compound interest long hand is a real chore. But it does register very clearly the most important point about compounding. See above and compare the difference in the level of interest earned between the first five years and the last five years of your investment. That’s compound interest in action.
If sums are not your strong suit, don’t give up, remember to use the Rule of 72
The basic principles of compound interest
So far we’ve only tackled lump sum investments, but what if you were a regular saver who was able to put away £100 a month over a long period of time, how well would you fare? Well, like a lot of things in life that would depend on a number of factors. But these basic principles hold true.
Start investing early
The more time you have, the greater the effect of compound interest. If you were to invest £200 a month from age 20 to 29 and then left your investment to grow, you would probably have more money at 60 than someone who chose to invest that same amount per month from age 30 to 59.
What difference does 1% make?
The difference between investing at, say, 7% and 8%, over time, is enormous so it's important you get the best rate you can. But it should be a rate on which you can rely.
Growing your savings
If you saved £100 a month for 40 years and your investments compound at 6% a year, you would not have £51,360, as you might expect (£100 x 12 x 40 x 106%), but actually £248,552!
There are various online savings calculators that can provide you with a quick, basic guide to show you how compound interest works with different financial products. Try the FSA’s website at www.fsa.gov.uk
