Thoughts from an active pensioner who is now somewhat past his Biblical "Use-by date"

"Why just be difficult, when with a little more effort you can be bloody impossible?"

Saturday, 29 May 2010

Premium Bonds or National Lottery?

I have had a number of Premium Bonds for some years, and when interest rates were higher, I got a small prize with reasonable regularity which gave me the equivalent of an acceptable rate of interest (particularly before I retired) and there was always the chance of winning a million!
However, with declining interest rates, and National Savings pretending that they are even lower that they are, I have not won a prize for some while, and of course my capital is depreciating with the current high inflation.
So currently there  seems some advantage of withdrawing my money and investing it in Index-Linked Savings Certificates. These currently pay 1% plus the rate of inflation, which would at least maintain the value of my capital.

Then the thought struck me; Suppose I "invest" the equivalent of the 1% interest each week in the National Lottery? Would I be better of than with Premium Bonds? Certainly I would be maintaining my capital, and in with a chance of a prize.

So let's invest a theoretical £10,000 in premium bonds. According to Money Savings Expert, with average luck this is likely to win me £100 in a year with a 1 in 338,824 chance of winning the £1,000,000 prize.

Now, the 1% on my £10,000 investment in Certificates would bring in a certain £100 per annum, the same as the most likely probability with Premium Bonds.

So what about the lottery? Well Lotto tickets cost £1 each, and so I could buy two a week with my interest money, but the calculations are somewhat more difficult, and I have to admit to not being interested in probability theory all those years ago when I took my "A Levels"!

However, according to the official statistics, the odds of winning the UK National Lottery jackpot prize are a staggering 1 in 13,983,816! The chances of winning any prize at all is around 1 in 54. 
So it seems that if one spends £100 each year, the above figures can be divided by 100 to give the probabilities of winning in the course of the year. Thus the chance of winning the jackpot comes down to 1 in 139,838, which is actually better than that of winning the top premium bond prize. Of course, there is no guarantee as to the size of the lottery prize, and it might have to be shared with other winners.
However, for the lowest prize, with £2 each week, statistically it seems one should win a couple of times a year, albeit a mere £10 minimum prize.

So all in all, Premium Bonds now seem to be a "no-brainer". Is there anyone out there whose maths is better than mine who can confirm my calculations?


  1. I'm afraid you lost me.

    Are you advocating the Lottery or Premium Bonds as the better investment?

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  2. Your system and odds appear to point to two separate stakes. Always wise to diversify?

  3. To me, £10,000 in Premium bonds will statistically bring in about £100 per year, but my £10,000 remains £10,000.
    If I put this in Index linked certificates, the £10,000 will go up in line with inflation and I will get £100 interest each year (at the end of 3 years).
    If I put the £100 on the lottery per annum, I am reasonably certain to get a small prize, maybe £20 or so, but I'm in for the big 'un. And with the present inflation my £10,000 will be £????
    Premium bonds are a gamble, so is the lottery. I think my later approach is better at this time if my mathematics is correct.

  4. Hi there. Just to point out your sums are a little shaky. Your odds of winning the national lottery should not be divided by 100 to get the odds of each draw over the year. Each draw your odds are the same, and they are huge- I just looked it up- it's 14 million to one however many times you play.
    The odds of winning on premium bonds changes with how many you have, but you quoted £100 giving you a one in 330000 of getting the million jackpot. And you're not actually spending the stake. Hugely better odds, and you keep your cash.
    To me, the bonds are still a better way to 'gamble' for fun, as you're not actually spending your stake. If you win nothing on the lottery, you're £100 down for the year.
    I think you're better off with Bonds.

  5. My maths is also week..I think by your post and comment i got also a clue about my calculations.

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