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As a teenager, I lost £5 to a card sharp in Oxford Street when I failed to find the lady. So I never gamble. Well, except once a month. I have a big chunk of my savings in premium bonds.

I am not alone. We own a record 58 billion of the £1 bonds. The number has grown nearly 40 per cent over the past five years. Two big boosts occurred in June 2014 when the maximum holding rose from £30,000 to £40,000 and a year later when it went up to £50,000.

More than 845,000 people have at least £30,000 in bonds; 340,000 of them have 40,000 or more and over 100,000 have the maximum £50,000. These investors hold £31bn in premium bonds — more than half the total.

Each month, the bonds earn interest at an annual rate of 1.35 per cent, which is put into a prize fund. That total is then shared at random among the bondholders as prizes. Each bond has a 1 in 26,000 chance of winning a prize in each monthly draw. Prizes are paid tax-free so the return is particularly good for higher or top-rate taxpayers.

The fund is divided so that 98 per cent of the prizes are for £25 and use up 84 per cent of the money. More than two million £25 prizes are paid each month. Other prizes range from £50 to £1m.

Although winning a million is a nice thought, forget it. You won’t ever win that prize. Even with the maximum £50,000 bonds you would have only an even chance of winning a million after 47,000 years. To put this in context, this would take us back to the time when humans stopped having sex with Neanderthals, and was a good 10,000 years before we started painting in caves.

The real attraction of premium bonds is those £25 prizes. With 50,000 bonds you will expect to win nearly 23 of those a year — almost two a month. Of course, chance will not produce an even return. But over time that should be the average. Here is the monthly record over two years of one large holding I am familiar with: 1,1,1,0,0,1,0,0,0,1,3,5,2,2,3,3,3,3,3,0,0,0,2,2. It is a good rate of return — so far rather better than the average you might expect. And all tax free.

When you deduct the cost of all the bigger prizes — and in a human lifetime you are highly unlikely to win anything bigger than £1,000 even with the maximum holding — then the return in £25 prizes is 1.13 per cent. If you add in the £50 and £100 prizes you might expect once every five years, this rises to 1.19 per cent.

For basic rate taxpayers that is equivalent to taxed interest of 1.49 per cent. For higher rate taxpayers the figure is 1.98 per cent, and 2.16 per cent for additional rate taxpayers. With the best rate elsewhere on instant access (which premium bonds are) around 1.6 per cent, these are attractive returns, especially for the better off.

The savings tax allowance of £1,000 for basic rate taxpayers and £500 for higher rate taxpayers from next April confirms premium bonds as ideal for the wealthy who are much more likely to have sufficient savings elsewhere to use up the new allowance.

However, small holdings are much less likely to win in any reasonable period. With the current minimum of £100 you might expect a prize every 22 years. But a single bond bought when Stonehenge was built would have won only about two prizes by now. And for a million pound prize? You would have to have bought it when oxygen first flooded the Earth’s atmosphere 2.4bn years ago to have a reasonable hope of winning by now.

Unlikely as it is for any individual, each month two lucky bondholders do win that rarest treasure — the million pound prize. And for those who do, NS&I sends Agent Million to their home to break the good news. Any prize of £5,000 or more merits a personal phone call. For the rest, winning numbers are posted online a few days into the month.

Ernie (electronic random number indicator equipment) who draws the numbers each month is not a computer. However hard they try, computers cannot produce genuine random numbers. Instead, Ernie uses a process, invented by a Bletchley Park codebreaker, called transistor thermal noise to create truly random events, which are then combined in turn into bond numbers (for more on this, you can follow Ernie on Facebook).

Every month the winning numbers are checked by the government actuary for randomness. Only after that are the prizes paid. As every bond has an equal chance there is no point in cashing in “unlucky” bonds and buying new ones. That just means you have a month between selling and buying when your bonds are not in the draw.

Anyone over the age of 16 can buy premium bonds online, by phone, or by post. They are no longer sold by the Post Office. Parents, grand and great grandparents can buy them for younger people, though the older generations must do so by post.

If all this has prompted you to check how the bonds your grandmother might have bought you are doing, go to www.nsandi.com where you can check results, trace lost bonds, and apply.

Paul Lewis presents Money Box on BBC Radio 4, on air just after 12 noon on Saturdays, and has been a freelance financial journalist since 1987

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