A long wait for a mammoth return on premium bonds

April was not a good month — even though I will pay less tax this year and I am lucky enough not to rely on frozen benefits or indeed frozen pay. But I did not win a prize in the April premium bond draw! That is unusual. The odds say I should win one or two prizes each month. I put a brave face on it because from next month — May — the prospects for us premium bond investors (but not for premium bond gamblers) are looking brighter.

That may seem odd because from May the interest rate on premium bonds falls from 1.25 per cent to 1.15 per cent. That interest is put into a fund which is used to pay out the prizes. The size of that fund is predicted to be about 10 per cent less in May than in April. But, and it is a very big but, I will be more — not less — likely to get a regular return on my investment.

Time to ’fess up. I like National Savings & Investments and I do have a lot of premium bonds. Having one or two — or that £100 your mum gave you or even the £5,000 you once bought with a bonus — is not really the essence of premium bond investing. You need loads: the maximum of £50,000. Then the law of large numbers (there really is one) begins to work. When I say “chances are you’ll win X prizes in Y years” that is more likely to be true in any given year the more premium bonds you have. If you had an infinite number it would always be true. But £50,000 is not a bad approximation.

Why does a lower interest rate and a smaller prize fund give me a bigger chance of winning? Or, to be completely accurate, a bigger chance of winning the smallest prize, that workhorse of premium bond investing, £25. Millions of those are paid out each month compared with just thousands of all the other prizes. In April a total of £70m was paid out in prizes. In May NS&I estimates that only £63m will be paid out. But there will be more £25 prizes — 55,124 more — taking the total from 2,117,718 in April to an estimated 2,172,842 in May.

The lower-value prizes of £25, £50 and £100 account for a fixed 90 per cent of the prize fund. But NS&I did confirm to me that the £50 and £100 prizes will be reduced in number, from more than 72,000 each in April to fewer than 21,000 in May, and that the number of £25 prizes will grow accordingly. That is why winning one of those will become slightly more likely.

If you had the maximum £50,000 bonds before May, you were likely to win 18.7 prizes of £25 per year. On May estimates that will rise to 19.6 per year. But you will wait more than five years for a £50 or £100 prize compared with well under two years before. Those three are the only prizes you need worry about. Before or after May it will still be a human lifetime (87 years now, it was 80 years) before you can expect to win £1,000 and several thousand years for a £5,000 or £10,000 prize. And the £1m pound prizes? Forget it. Ice ages are more frequent.

So that £25 workhorse is going to plod along a little more quickly from May. The effective rate of return if you only ever win £25 prizes is 0.98 per cent. Tax-free. Which is the same as 1.22 per cent if you pay basic rate tax and 1.63 per cent if you pay higher rate tax. Before May it was 0.93 per cent.

Of course the first £1,000 of interest on all your savings is tax-free anyway (£500 for a higher rate taxpayer). But I am guessing that if you have £50,000 to put into premium bonds you probably have a quite a bit of other cash sloshing around and have already used up that allowance.

If you are really lucky and pay the 45 per cent additional rate tax then you don’t have a personal savings allowance anyway. Even without a tax saving, a premium bond interest rate of 0.98 per cent is not bad for an instant access account — just outside the top five and better than the 0.75 per cent NS&I pays from May 1 on its income bonds.

So that is why I say the new structure will favour investors rather than gamblers who will wait even longer for the big prizes.

If you had bought £50,000 in premium bonds to celebrate killing one of the last woolly mammoths 12,500 years ago you might expect to have won one £25,000 prize by now. Your even more distant ancestor who did the same after she spent a passionate night with one of the last Neanderthal men 55,000 years ago might expect to have won one £1m prize by now and probably one £100,000 one as well. As I am 2.3 per cent Neanderthal I like to think she was an ancestor. From May the £5,000 prizes only come along every 2,361 years and £10,000 every 4,825 years — so you’d be lucky to have won once since the Great Pyramid at Giza was built. On average. If you have the max.

If you just have the £100 your Mum gave you on your fifth birthday with visions of you being a millionaire one day then you will be 30 before you get your first £25 prize. You will need more than the patience of a saint or even one of the first saints, the prophet Ezekiel from around 600 BCE, to get a £100 prize (once in 2,677 years) and you will wait nearly 28m years to get the big £1m. If you had bought 10 premium bonds the year the dinosaurs were wiped out 66m years ago you would probably have won just one £25,000 prize and nothing bigger.

So premium bonds are a rubbish gamble. Forget the big prizes; they will never be yours. But max out and check them every month for that small, tax-free income stream that is guaranteed. Not just by the UK government but by the laws of mathematics.

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. Twitter: @paullewismoney