Premium Bonds Are they worth it?

This unique article separates Premium Bond fact and myth, using the UK's only Premium Bond probability calculator. Nearly half the UK has money in these bonds, they generate cash for the government and with over £42 billion held in them, are by far the biggest single savings product around. But are they worth it?

Our specially-developed Premium Bond Calculator reveals what your realistic chances of winning different amounts are, depending on how many bonds you have and how long you hold them. Then it enables you to compare this to a top savings account 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 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 (it used to be just £31,700 of the first £35,000, then £50,000 until 31 December 2010).

  The maximum you can put in bonds is £30,000, which means on its own, it would be protected in any UK-registered account (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 or guardians and grandparents (but not anyone else).

• Winnings can be re-saved. Rather than receiving the winnings, you can opt to have them 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; in other words, 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 a million is over 40 billion to 1. Of 40 billion pounds in Premium Bonds, each month, there are over 1.7 million prizes given out of between £25 and £1 million each. Over 1.6 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 £39 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 article).

  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 - after that they just sit there. If you believe a late relative had bonds, check it out as soon as possible.

Are they any good?

There's heavy positive spin put out about Premium Bonds, after all NS&I is government-backed, and they help generate government funds and cash flow. Yet the payout is much worse than many believe.

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.

They're worse than the top savings accounts

Even if we assume you would win the £1 a year for every £100 saved, and compare this to the Top Savings Accounts or Cash ISAs, it's usually disappointing.

How Premium Bonds compare (May 2012)

		Returns based on £1,000 over a year
	Interest rate	Non taxpayer	Basic tax	Higher tax
Premium Bonds (1)	1.5%	£15	£15	£15
Top savings account	3.1%	£31	£24.80	£18.60
Top cash ISA	3.5%	£35	£35	£35
(1) Someone with average luck is actually likely to win less than this

Clearly, even if you did get the interest rate, compared to a tax-free cash ISA you're always on a loser, plus the very top paying savings accounts beat it too.

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 you're 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 41 billion chance of becoming a millionaire through the Premium Bond draw.

The fact the payouts are commonly referred to as a 'win' rather than an 'interest payment' is psychologically devious. Comments like "my friend wins £25 every few months" mislead. On clinical evaluation, someone with £10,000 of bonds should 'win' £150 a year; that's £25 every two months. Yet the same cash in a savings account would 'win' around £25 every month (£300 a 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?

Look at Premium Bonds with a clinical financial eye and, as we've already explained, they're currently not worth considering in terms of return. Yet some will win more than the average. Not many, but a few.

Put £100 in Premium Bonds, calculate the probability and 95% of 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.

Premium Bonds aren't 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.

Prize Distribution (last updated 1 May 2012)

Prize Level	Amount per month	Odds of winning per £1 bond
£1 million	1	1 in 43,474,820,688
£100,000	5	1 in 7,245,841,249
£50,000	8	1 in 3,105,363,428
£25,000	18	1 in 1,358,596,526
£10,000	46	1 in 557,372,901
£5,000	91	1 in 258,780,286
£1,000	1,089	1 in 34,641,512
£500	3,267	1 in 9,626,900
£100	31,978	1 in 1,192,961
£50	31,978	1 in 635,880
£25	1,745,951	1 in 24,000
£0	43,546,384,150	Virtual certainty

Why most people win less than the interest rate

Even though Premium Bond rates stack up poorly compared to decent savings rates, even that's still misleadingly generous. The real expected payout is much less, as it's massively skewed by the distribution of the prizes.

This is tricky to understand, so let me start with a simple example. Suppose a contest offered a £1,000,000 prize and allowed a million people to buy a ticket costing £1. It could then be argued the average winnings per ticket were £1, even though 999,999 people would win nothing.

A similar, though less drastic, effect is happening with the Premium Bond interest rate. It says the payout is 1.5%, so you'd expect to win £1.50 per £100. But this is impossible, there isn't a £1.50 prize; you can either win nothing, £25, or more than £25. The big jackpot prizes, won by a minuscule number of people, skew the payout average and make the interest rate look much more generous than it is.

The Premium Bonds Calculator takes all this into account, and through statistical analysis, reveals what you're really likely to win. The stats it throws up aren't pleasant reading for Premium Bond holders.

• £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 out of every 20 people with this amount 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 110,000.

Let's get 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 someone with 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. Yet to win more than £500 holds scores of variables.

Plus of course, the draws are monthly, so if you're calculating the assumed winnings over five years, it actually means you're calculating the interaction of probabilities for over 60 draws to get the various answers. This is why, until now, the probability was 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.

How do premium bonds stack up? (as of May 2012)

Amount of bonds	Odds of winning £0	Chance of beating inflation (RPI)		Chance of beating a savings account
		Amount needed to beat inflation	Odds of earning this or more with Premium Bonds	Basic rate		Higher rate
				Interest in savings account (1)	Odds of earning this or more with Premium Bonds	Interest in savings account (1)	Odds of earning this or more with Premium Bonds
Over 1 year
£100	95% chance	£3.60	1 in 20	£2.48	1 in 20	£1.86	1 in 20
£1,000	61% chance	£36	1 in 10	£24.80	1 in 2.5	£18.60	1 in 2.5
£5,000	8% chance	£180	1 in 100	£124	1 in 7	£93	1 in 3.5
£30,000	1 in 3,270,061	£1080	1 in 166	£744	1 in 18	£558	1 in 5
over 5 years
£100	78% chance	£18	1 in 5	£12.40	1 in 4.5	£9.30	1 in 4.5
£1,000	8% chance	£180	1 in 100	£124	1 in 7	£93	1 in 3.5
£5,000	1 in 268,409	£900	1 in 100	£620	1 in 23	£465	1 in 6
£30,000	Negligible	£5400	1 in 166	£3,720	1 in 83	£2790	1 in 10
(1) Top saving account paying around 3.1% interest, it assumes the interest is withdrawn, not compounded as this is how most people use premium bonds. Note where the odds are better than 1 in 2, they are expressed as a percentage

For example 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 I can come up with is: put £1000 in a savings account and a basic rate taxpayer earns £24.80 in a year; therefore 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 £1,100 in a savings account earns £27.28, to beat this takes at least 2 x £25 wins or 1 x £50 win, even though there's only 100 quid more, thus the odds of winning less jumps to 88%.

In summary: The results

Look at Premium Bonds with a clinical financial eye and they're only worth considering as a serious place to put savings if you're a higher 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 beware, it ain't pretty reading.