Premium Bonds Are they worth it?

Nearly half the UK has bonds - they're by far the biggest savings product with over £44 BILLION in 'em - but are they worth it? We want to separate fact and myth, using the unique Premium Bond Calculator.

It reveals your real chances of winning different sums, based on how many bonds you have and how long you hold 'em, then compares with top savings and inflation.

The basics: How do Premium Bonds work?

Premium Bonds are simply a savings account you can put money into (and take it out when you want), where the interest paid is decided by a monthly prize draw. You can win between £25 and £1 million, tax-free.

The minimum holding is £100 (or £50 for monthly standing orders) and the maximum is £30,000. So put a grand in and you get 1,000 £1 bonds. Each of these is then individually entered into the prize draw. They can be bought online at NS&I's website, in post offices, over the phone, by post or through a regular monthly payment by standing order.

The bonds enter the prize draw one calendar month after purchase and continue until you cash them in, which can be at any time, though it takes up to eight days to get hold of your cash.

Some quick Premium Bond facts:

• The capital is very safe. You don't risk the money you put in, only what interest you'll get. Premium Bonds are operated by NS&I which, rather than being a bank, is backed by the Treasury, meaning you get 100% safety for your cash.

  However, NS&I can't play this card as strongly as it used to. The state now guarantees every UK-regulated savings account up to £85,000 per person, per institution (previously just £31,700 of first £35,000, then £50,000 until 31 Dec 2010).

  The maximum you can put in bonds is £30,000, which means it would be protected in any UK-registered account anyway (read the full Are Your Savings Safe? guide).

• Who can buy them? Anyone aged over 16 can buy Premium Bonds and they may be held in the name of under-16s by parents/guardians. Grandparents or great-grandparents can buy then nominate the child's parent or guardian to hold them.

• Winnings can be re-saved. You can opt-in to have winnings automatically buy more bonds. This works in a similar way to compound interest in a normal savings account, as then your winnings have a chance of winning.

• The winners are decided by random draw. NS&I sexes-up the draw by the personification of the IT equipment; it calls it ERNIE (Electronic Random Number Indicator Equipment). In reality it's a simple, audited, random number process where every bond has an equal chance of winning no matter where or when it was bought.

• In a typical draw, each bond's chance of winning £1m is over 44 billion to 1. Of £44 billion in Premium Bonds, each month, there are almost 1.9 million prizes given out of between £25 and £1 million each. Over 1.8 million of these are £25, 30,000 are £50 and £100 and the remaining 5,000 or so are between £500 and a million (only one is £1 million though).

• Claiming old prizes/bonds. There are currently £44 million-worth of prizes unclaimed. To check if any are yours, go to the NS&I website. There's no time limit to claims (also read the Reclaiming Lost Assets guide).

  Premium Bonds can't be passed on, so either use them or cash them in. If a Premium Bond holder dies, the bonds only remain eligible to win for 12 months. If you believe a late relative had bonds, check it out as soon as possible.

Are they any good?

There's heavy positive spin about Premium Bonds, after all NS&I is state-backed, and they help generate Government funds and cash flow. But in pure cash terms, they're worth considering as a place to put savings if you're a higher or additional rate taxpayer, but basic-rate and non tax-payers are unlikely to win enough to beat the odds.

You're likely to win even less than the interest rate

The value of prizes paid out is determined by an interest rate, which is currently 1.5%. It usually changes when the Bank of England base rate changes. If you owned every Premium Bond in existence, the amount won over a year would be equal to 1.5% of what you put in. So very roughly, for every £100 put into Premium Bonds on average, you'd expect a £1.50 annual return.

Yet because of the way the prizes are allocated, the majority of people will win much less than the interest rate anyway. There's a full explanation of why this happens later, but for now you can use the Premium Bond Probability Calculator to see how likely you are to win an amount equal to the interest rate.

For many, they're worse than the top savings accounts

Even if we assume you would win the £1.50 a year for every £100 saved, and compare this to the Top Savings Accounts or Cash ISAs, basic rate (or non-)taxpayers can still usually beat it in a normal savings account.

However, historically low savings rates mean that for higher-rate taxpayers (those who pay 40% income tax) or top-rate payers (45%), the AVERAGE return on Premium Bonds are not awful - and those with rough typical luck stand an OK chance of beating the top easy access accounts.

Don't think of it as 'winning'

The great sell is 'the lottery effect', the chance of winning a dream, and a million. Equally you could be the next space-walking astronaut, and your odds probably aren't that dissimilar! Your chance of winning the jackpot per £1 spent on the lottery is one in 14 million, far-outstripping the one in 44 BILLION chance of becoming a millionaire through the Premium Bond draw.

The fact payouts are commonly called 'wins' and not 'interest payments' is psychologically devious. Comments like "my friend wins £25 every few months" mislead. On clinical evaluation, someone with £10,000 of bonds should 'win' £100 a year; that's £25 every three months. Yet the same cash in a savings account would 'win' a guaranteed £140 EVERY year.

You can easily compare how much you are likely to make with Premium Bonds to inflation and the top savings accounts by using the Premium Bonds Calculator.

Are they ever worth it?

Once you're looking with a clinical financial eye, Premium Bonds are never all-star winners - though higher- and top-rate taxpayers have a much better chance of beating standard savings than others.

Some people will win more than the average. But it won't be many. Put £100 in Premium Bonds, calculate the probability and 19 in 20 people won't win a penny over a year, but one in 20 will win £25 or more! If you're that lucky person, this is a great return. Yet the odds of winning big get very long; use the calculator to gauge your chances.

They're not as good as they first appear

It's all about the actual prize distribution. Below is the distribution of prizes in a typical monthly draw. This can and does change (for example, sometimes there are extra £1 million prizes in promotional draws), but the number's still relatively low and doesn't change the chance for most.

Why most win less than the interest rate

With savings rates so low, Premium Bonds do not look like a bad investment for higher and additional rate taxpayers. However, real expected payouts are much less, massively skewed by the prize distribution. This is tricky, so let's start with a simple example.

A contest offers a £1,000,000 prize and lets a million people buy £1 tickets. It could then be argued the average winnings per ticket were £1, even though 999,999 people would win nothing.

The Premium Bond interest rate creates a similar, though less drastic, effect. It says the payout is 1.5%, so you'd expect to win £1.50 per £100. But that's impossible, there isn't a £1.50 prize; you can either win nothing, £25, or more than £25.

The jackpots, won by a tiny number of people, skew the payout average and make the interest rate look far more generous The Premium Bonds Calculator cuts through this; its statistical analysis reveals what you're really likely to win - not always pleasant reading for bondholders.

• £100 over a year. Put the minimum £100 in, and the interest rate predicts a win of £1.50 over a year - impossible as the smallest prize is £25. In fact, 19 of every 20 people with £100 in won't win a thing; leaving only one in 20 winning £25 or more.

• £1,000 over a year. Put £1,000 in Premium Bonds over a year and while the interest rate predicts a £15 win, the majority of people (61%) still win nothing.

• £30,000 for a year. Even if you put the biggest amount you're allowed to in Premium Bonds, your chance of winning the million in a year is still 1 in 122,000.

Really nerdy: Bizarre probability outcomes!

On the surface, Premium Bonds don't look complex. NS&I happily lists enough data on its website to allow anyone with a calculator to work out the chance of one bond winning a £25 prize over a month (1 in 24,000, by the way).

To work out the chance of five thousand bonds winning £500 or more includes countless variables. To win £500 in one go could be one £500 prize, or five £100 prizes, or ten £50 prizes, or twenty £25 prizes; or a combination of them - making the maths incredibly complex!

Plus, the draws are monthly, so if you're calculating winnings over five years, it actually means you're calculating the interaction of probabilities for over 60 draws to get the various answers, making the probability virtually impenetrable. In the end we cracked it using a very advanced multinomial probability equation devised by a post-doctoral cosmology statistician!

And if you look at the outcome of this in practice, when you look at the table below you'll see some rather bizarre results.

For example, over one year, you have more chance of beating savings rates holding £5,000 than you do with £30,000. And over five years, you've more chance of beating a savings account interest rate with £1,000 than with £5,000.

All but stats nerds should skip the explanation coming next, as it really is quite esoteric.

This is because the likelihood of winning peaks at or just under a payout value which can be made up from a combination of prizes, so where the amount needed to beat the savings account is only just above one of those, the odds of beating it increase.

The easiest example we can come up with is: put £1,000 in a savings account, and a basic rate taxpayer earns £14.40; so a Premium Bond holder only needs one £25 prize to beat it, and the chance of winning less than this is 60.7%. Yet someone with £1,750 in a savings account earns £25.20, to beat this takes at least 2 x £25 wins or 1 x £50 win, even though there's only 750 quid more, thus the odds of winning less jumps to 85%.

In summary: The results

Look at Premium Bonds with a clinical financial eye and they're worth considering as a serious place to put savings if you're a higher or additional rate taxpayer who has used up your Cash ISA allocation.

Yet for those who like a flutter, as Premium Bonds do protect your cash, it's fine to put a non-significant portion of your money in them, more for fun than returns. Before deciding, use the calculator to look at the real odds. If you're willing to take the gamble after that - then it's fine.

Many people often think "I'm likely to get about 1.5% and there's a small chance of winning a million". But the main point is this isn't correct. You're actually likely to get quite a lot less than 1.5%, and there's a negligible chance of winning a million.

Take a look at the chances, but for most, savings are still a better home for your money.