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23 April 2021
Line up everyone with £1,000 worth of Premium Bonds in order of their year's winnings, and the person halfway along would have won… not a penny! In fact, you'd need to walk past 70% of the line until you hit the first £25 winner.
Premium Bonds are the UK's biggest savings product, with more than 21 million people saving over £100 BILLION in them. Yet the prize rate was slashed in December 2020 – so is it still the right thing to do? MoneySavingExpert.com's Martin Lewis uses exclusive statistical analysis to tackle the big question – are Premium Bonds worth it?
NS&I Premium Bonds are a savings account you can put money into (and take out when you want), where the interest paid is decided by a monthly prize draw. You buy £1 bonds and each has an equal chance of winning, so the more you buy, the more your chances improve.
The distribution of prizes changes each month. Below is a table of the typical current distribution:
|£1 million||2||1 in 51,063,525,579|
|£100,000||5||1 in 14,589,535,102|
|£50,000||8||1 in 6,808,445,741|
|£25,000||18||1 in 3,094,747,872|
|£10,000||45||1 in 1,309,316,283|
|£5,000||91||1 in 604,299,713|
|£1,000||1,702||1 in 54,583,991|
|£500||5,106||1 in 14,637,617|
|£100||27,651||1 in 2,949,251|
|£50||27,651||1 in 1,639,825|
|£25||2,897,916||1 in 34,500|
Rather watch than read? Here's my Premium Bonds explainer from my TV show...
The clip below has been taken from The Martin Lewis Money Show on 3 December 2020, courtesy of ITV Studios Ltd, and lasts three minutes and 50 seconds. All rights reserved. You can turn on subtitles by selecting the keyboard image on the bottom right of the video.
Just bear in mind the savings rates mentioned are subject to change. For the most up to date rates, see our Savings guides.
In general, you need to hold the bonds for a full month before they're eligible to win. So, buy bonds any time in January and they'll be in the draw from March. So if you're moving money over from other savings, it's best to do it in the last week of the month, as that way you minimise the time the money's not earning interest and also not in a draw for Premium Bonds.
The exception to this is if you reinvest your prizes – these bonds will be in the draw from the month after you win. So, let's say you won £25 in January and had reinvesting set up – the new £25 worth of bonds would be in February's draw.
They continue to be eligible until you cash them in, which can be at any time, though it can take up to eight working days to get your cash.
There's also an urban myth that newer bonds have a higher chance of winning. But, every bond has an equal chance of winning, no matter where or when it was bought.
My suspicion of why people think this is because it used to be possible just to buy a £1 bond; now the minimum is £25 (and until Feb 2019 was £100). So people who have bought more recently tend to have more bonds which means they will tend to win more often.
Premium Bond prizes (the interest) are paid tax-free. However for most people that's no longer a bonus.
Since 2016, the personal savings allowance (PSA) has meant all savings interest is automatically paid tax-free. You only need to pay tax on it if you're a basic 20% rate taxpayer earning more than £1,000 interest a year, a higher 40% rate taxpayer earning more than £500 interest a year, or a top 45% rate taxpayer.
In practice this means more than 95% of people no longer pay any tax on their savings interest – and for those people Premium Bonds therefore no longer have a tax advantage.
For those who will pay tax, there is a decent advantage of Premium Bonds as prizes do not count towards the PSA, so it's almost an extra allowance in its own right (assuming you win something, of course).
The nearest thing Premium Bonds have to an interest rate is their annual prize rate, currently 1%. The interest rate describes the "average" payout, but it is just a vague watermark.
It describes the 'mean' average, indicating that for every £100 paid in to bonds, on average £1 a year is paid out – yet in practice this is impossible, as the smallest prize is £25. In fact the Premium Bond Probability Calculator shows if 30 people each had £100 invested, for one to win £25-plus, the remaining 29 would have to win nothing.
A far better indication of what someone with typical luck would win is the 'the person halfway along' measure. Those who can dredge up their school maths will remember this is called the median.
Why the Premium Bond prize rate isn't what you'll win
To show you why using the 'mean' average isn't a good description of what most people will win, let me use an extreme example…
Imagine I sold a million people a £1 lottery ticket, and then paid just one winner a million pounds.
I could argue, mathematically, that the average (mean) payout was £1, so on average everyone got their money back. This, of course, is bonkers.
Almost everyone wins nothing – which is the median average – as if you lined them all up and asked, the midway person would've won nowt.
So to really see average luck you need to focus on this 'median' average returns figure. And for the rest of this guide whenever I refer to average luck, that's what I mean..
With Premium Bonds, for every person who wins £1 million a lot of people have to win nothing. So the median average will always be lower than the mean average.
Yet as you can see the more bonds you have, the more likely you are, with average luck, to win closer to the prize rate – though most people will always win less than it.
Unless you're a stats nerd, avoid this answer, it's going to get tricky.
Doing this table was actually incredibly hard. Even the Premium Bond Probability Calculator doesn't automatically show exact median winnings. So to be accurate I had to pick amounts where I had a high degree of confidence in the right answer - ie the calc showed around a 50% chance of winning a prize level. Hence picking £16,000 and £21,500, rather than more rounded amounts.
In general, the more you have, the closer to the prize fund your median return is. But exactly at what amount the median hits is lumpy because it jumps at £25 a time, so vagaries of the statistics mean it doesn't rise in a purely linear way. (If you don't get this, use the calculator for different amounts and see where 50% probability is likely to be.)
With Premium Bonds there is no risk to your capital – so the money you put in is totally safe – it is only the 'interest' that is a gamble. And as Premium Bonds are operated by NS&I which, rather than being a bank, is backed by the Treasury, this capital is as safe as it gets.
This safety used to be a big boon because you didn't get the same protection with other savings. However, under the savings safety rules all UK-regulated savings accounts are now protected up to £85,000 per person, per institution by the Financial Services Compensation Scheme (FSCS) – and the maximum you can put in Premium Bonds is £50,000.
In practice, isn't NS&I still safer though?
Technically yes as there is one difference. As NS&I is owned by the Government it simply won't go bust. Well, unless the Government itself goes bust that is, in which case we will have bigger problems.
Other savings institutions may go bust, and if this happened, if no rescue measures succeeded, in that extreme event you'd have to claim back your capital and interest from the FSCS.
The FSCS scheme aims to usually pay out on savings within seven days. So, yes, arguably there are tiny benefits on safety from NS&I as it should never go bust, therefore there could never be a situation where you have to wait to get your money as there could be for a few days with other savings – though, ironically, while NS&I aims to get you your money back within two working days, there have been delays with its systems in recent months.
On the surface, Premium Bonds don't look complex. NS&I happily lists the chance of one bond winning a prize in a month (1 in 34,500) on its website.
Yet to accurately calculate the odds of winning certain prize levels, you need to use something called "multinomial probability". After all, to work out the chance of someone winning £200 a year, they could win 2 x £100, 8 x £25, 4 x £50, or a host of other variants. This multitude of probabilities means accurate calculation is hellish.
Back in 2012 I set myself a challenge to do it. I failed. I got one of my team with a top maths degree to try. He failed. We contacted a London School of Economics professor of financial mathematics – she knew how to work it out, but she needed a specialist to do it for her.
Eventually we tracked down a post-doctoral cosmology statistician (someone who calculates star movements) who had the requisite probability skills, and he wrote us an algorithm to build the Premium Bonds Calculator.
This allows you to plug in how many bonds you have, and it will predict your likely winnings and compare them with savings. It proves that at every value someone with typical luck will earn less than the quoted prize rate.
The odds in the calculator are based on the prize distribution for the most recent draw; it does change slightly each month. So even with all the great maths, even this should only be seen as a very good estimate.
The personal savings allowance means that basic-rate taxpayers can earn £1,000 of interest a year tax-free (£500 for higher-rate taxpayers, nothing for additional-rate taxpayers).
So that makes the Premium Bond rate very easy to compare with other savings (rates correct at 1 March 2021). Let's start by simply using the prize fund rate of 1%.
The Premium Bond rate is currently higher than almost all savings rates, but the prize rate's almost irrelevant to what you actually win, so the question still stands: "Should I move cash to Premium Bonds or top savings?"
Let's stick with the prize rate for now (even though in practical terms it is almost impossible to win some of these amounts) and see how it compares in real terms with the best on the market.
|Premium Bonds (1)||£10||£50||£200|
|Top easy-access ISA||£4||£20||£80|
|Two-year fixed savings||£7.50||£37.50||£150|
|Two-year fixed ISA||£6.20||£31||£124|
|(1) Someone with average luck is actually likely to win less than this, and the prize distribution means you can't actually win these amounts. Rates correct at March 2021.|
As you can see, Premium Bonds are actually now top of the tree in terms of rates alone.
However, that's when I exaggerate what Premium Bonds are likely to pay by utilising the prize rate. As I explained earlier, if you have average luck you won't win as much as the 1% prize rate, so let's compare the predicted returns using the Premium Bond Probability Calculator.
|(1) Top easy-access savings account paying 0.5% interest, it assumes the interest is covered by your personal savings allowance up to your limit, and that it is withdrawn, not compounded, as this is how most people use Premium Bonds. Rates correct at March 2021.|
So, when comparing Premium Bonds against simple top standard savings, you're actually more likely to win with savings for lower amounts. Yet once you've more than £5,000 saved in Premium Bonds, you're actually more likely to win close to the prize rate, and therefore Premium Bonds do look a little better – though you'll need to have this average luck to beat savings.
As we worked out above, Premium Bonds come into their own for those with larger amounts of savings in them. This is especially true if you're a higher-rate or top-rate taxpayer and pay tax on your savings interest, which assumes you've used up your personal savings allowance (PSA). If that's the case, a basic-rate taxpayer only gets 80% of their interest, a higher-rate taxpayer 60% and a top-rate taxpayer 55%.
Yet money made from Premium Bonds, like cash ISAs, is always tax-free and does not count towards the personal savings allowance, so it's almost like an extra allowance.
Let's start by simply using the Premium Bond prize fund rate of 1% – even though, as explained already, most people won't win that much.
|Premium Bonds (1)||1%||1%||1%||1%|
|Top easy-access ISA||0.4%||0.4%||0.4%||0.4%|
|Two-year fixed savings
|Two-year fixed ISA||0.62%||0.62%
|(1) Someone with average luck is actually likely to win less than this. Rates correct at March 2021.|
Now let's take the analysis up a step, and look at how likely you are to beat top savings with Premium Bonds.
|Basic-rate taxpayers||Higher-rate taxpayers|
|£30,000||1 in 34,028||£120||98%||£95||99.3%|
|£50,000||1 in 35.7m||£200||99.6%||£150||100%|
|(1) Top easy-access savings account paying 0.5% interest, it assumes the interest isn't covered by your personal savings allowance, and that it is withdrawn, not compounded, as this is how most people use Premium Bonds. Rates correct at March 2021.|
So overall, the higher tax band you're in, and the more money you are saving in Premium Bonds, the better a bet they look for you.
All my comparisons with savings products above are based on somebody who has average luck and indeed that is the sensible way to assess this. However it is impossible to ignore the fact that some will have better than average luck, and indeed that does need to be factored in to your decision.
Certainly if there is only a marginal difference in the amount you are likely to earn from savings compared with Premium Bonds, then you can factor in "the chance of winning large" as an additional fringe benefit of Premium Bonds, and it wouldn't be too bad to let that sway your decision marginally.
Equally you may decide that you like a punt, and even if the odds are great, then putting a non-substantial portion of your savings into Premium Bonds isn't too bad an idea. But I would always use the Premium Bonds Calculator first to see what your real chances are.
And you do even have a chance of winning £1 million; then again you could also toss a coin and see it land on its edge.
Your chance of winning the jackpot per ticket on the National Lottery is one in 45 million in a week, far outstripping the one in more than 51 BILLION chance of becoming a millionaire through one single Premium Bond in a month. Of course though, the more bonds you have, the more chance you have of winning.
Plus, bonds are entered into the draw every month, rather than as a one off. Here are your odds of winning the jackpot over a year.
|£100||1 in 42,541,099|
|£1,000||1 in 4,249,850|
|£5,000||1 in 849,505|
|£10,000||1 in 424,057|
|£30,000||1 in 140,668|
|£50,000||1 in 84,037|
This lottery-effect hooks you into the unlikely dream of bagging a million-pound prize.
I often hear excited comments such as: "My friend wins £25 every few months!" Yet someone with £10,000 worth of bonds should win £75+ a year – that's £25 every few months.
Don't just rely on your memory of what you won, though. The win effect means people remember the good months. Take a look and calculate what you're actually winning to see how it'd compare with top savings – and how good your luck has been.
If you save money anywhere and it doesn't grow as quickly as prices are rising, then in real terms your savings are actually shrinking not growing. Inflation is the measure of prices rising, so if your savings pay more than inflation then they're growing, if not they're shrinking.
Yet due to the coronavirus pandemic inflation's sharply dropped, so at the moment you have a good chance of beating inflation if you have a decent amount saved in Premium Bonds, and you have average luck. Again, if you've smaller amounts saved, you're less likely to beat inflation.
When you win with Premium Bonds, rather than taking the cash, you can simply arrange for the money to be reinvested (unless you already hold the maximum £50,000). In other words, your winnings will buy more bonds. That increases your holding, and therefore increases your chances of winning.
If you are going to put money in Premium Bonds and you don't need the cash, then this is a sensible move, as it is effectively like compound interest in a normal savings account. The hope is you get growth on the growth (or here, prizes on the prizes).
You can check if any are yours via the NS&I website – there's no time-limit to claims, so you can go back as far as you like.
You'll need your Premium Bond holder's number – just enter this on the website above. You can choose to check the latest draw, the last six months, or any unclaimed prizes.
For full information and other ways to claim if you don't know all your Premium Bond details, see our Unclaimed Premium Bond prizes news story.
Premium Bonds can't be passed on. If a Premium Bond holder dies, the bonds only remain eligible to win for 12 months. So the only way to pass them on is to cash them in and then that forms part of the deceased's estate. The executor will need to cash the bonds in to be able to distribute them to the beneficiaries.
However if prizes were won before the 12-month limit, they can still be claimed with no time-limit.
Premium Bonds aren't inheritance tax free, so if the capital tied up in them forms part of the estate and is passed on, they may be taxed (see our inheritance tax guide for when you might need to pay).
Another potential snag I've heard of is that you may need to get probate on the bondholders' estate if the Premium Bond holding is over £5,000, even if it's not needed to release the rest of the estate's assets held with other organisations. For more, see NS&I's guide.
Look at Premium Bonds with a clinical financial eye and they're actually not a bad bet for some. Here's my take on who they're best for:
A final thought: Premium Bonds are all about your mentality. They do protect your cash, so even if the returns don't look a good bet, it's fine to put a non-significant portion of your money in them, provided you're aware it's 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% and there's a small chance of winning a million". But the main point is that this isn't correct. You're actually likely to get less than 1%, and there's a negligible chance of winning a million. If you know and you're OK with this, then investing in Premium Bonds isn't a bad plan.
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