Premium Bonds: what can you earn from Ernie? In 2009 NS&I decided that Ernie (Electronic Random Number Indicator Equipment - a machine which generates random numbers electronically) would pick just one £1m winner each month rather than two. Unsurprisingly, Premium Bonds divide advisers, as well as investors, between pragmatists who loathe them and optimists who see the attraction of the chance of a big win, and view them as a bit of harmless fun. Steve Wilson, an adviser with Alan Steel Asset Management, said: "They are a complete waste of money. We have plenty of clients with them who never seem to win anything, or not very much. They always remember when they get the odd £50 win, but even if you add up these little wins, they never amount to a proper return. But Patrick Connolly, a financial planner at AWD Chase de Vere, said: "We think they are fine for the right people. They are particularly good for higher-rate taxpayers, who do not need to generate an income but are concerned about the security of their money. There is absolutely nothing wrong with having a bit of money in the bonds, and there is always the prospect of a decent win. Many continue to hold bonds for decades for sentimental reasons, long after giving up hope of a win, perhaps because they were bought by an aunt or grandmother as a birthday present. One Telegraph reader, Simon Hunter, recently received his first prize cheque from his Premium Bonds. Considering he had held the £10 holding for 27 years, a £25 cheque may seem like a pretty paltry return. But he has calculated that this equates to a compound annual return of 4.75pc. As they are tax-free, this is worth 7.9pc to a 40pc taxpayer, and 5.9pc for 20pc taxpayer. Mr Hunter, from Edinburgh, said: "That's not too bad, particularly when you remember it is tax-free." Danny Cox, a financial adviser with Hargreaves Lansdown, did even better. His grandmother bought him a £5 bond for his christening in 1965. Thirty years later, in 1995, and shortly after she died, he won £500. That equates to 16.59pc compound annual return over the same period, equivalent to 20.7pc for a basic-rate taxpayer and 27.6pc for higher-rate payers. Mr Cox said: "That is a surprisingly good return. Moneyfacts put the average savings account over that 30-year period paying 8.9pc, which would have been taxed. So the return from these Premium Bonds nearly doubled that as an investment. Other recent winners picking up prizes after a long wait include a Somerset bondholder who received a £1,000 surprise after investing £40 in 1958, shortly after Ernie was launched, equating to a 6.1pc annual return. Elsewhere, a Wirral saver collected £5,000 after investing £3 in 1973, equivalent to a 20.8pc annual return. So sometimes it pays to wait, not least as the prize money tends to rise with inflation. At outset in 1957, the top prize was £1,000, compared with today's £1m. And the odds of winning aren't quite so dire if you have a larger holding. With the maximum £30,000, you only have a one in 1.5 million chance of scooping the million, but you have a 70 pc chance of winning any prize. But Mr Wilson remains sceptical. He said: "They talk about odds, and how much you can expect to earn, but it all seems nonsense to me. As far as I can see, no one earns very much at all. But the alternatives are not great either. The best savings accounts are currently paying between 2.5pc to 3pc before tax, which falls to about 1.5pc to 1.8pc after tax for a higher-rate taxpayer. Tax can be avoided by saving in a cash Isa, but this is restricted to £5,640 per year. The best cash Isa rates include a 60-day notice account with Coventry Building Society paying 3.25pc and an M & S Isa paying 3pc. NS&I's own direct Isa pays 2.5pc. So even their biggest fans do not recommend Premium Bonds as the first home for your savings. Mr Connolly said: "First everyone should use up their Isa allowance each year." How to buy Premium Bonds Anyone aged over 16 can buy Premium Bonds from any post office, online at nsandi.com or by telephone on 0500 007007. Alternatively, you can collect an application form from the Post Office and send it to Premium Bonds, National Savings and Investments, Glasgow G58 1SB. The minimum purchase is £100, for which you receive 100 bonds, and the maximum £30,000. New bonds do not enter the draw until after a full calendar month, so if you buy in March, they will be eligible for the May draw onwards. If you want to buy bonds for a child, you must nominate one of their parents to manage the bonds and receive the prize money. NS&I has an online prize service which allows you to check your numbers. Prizes can now be paid straight into your bank account or small prizes are sent by warrant, so it is vital to ensure your address is up to date. If they are not claimed within six months they are redespatched. After that, they enter the unclaimed fund. There are 811,000 prizes currently unclaimed, worth £4m. Unclaimed prizes can be claimed at any point.