## Are they worth it?

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 almost two-thirds of the line until you hit the first £25 winner.

Premium Bonds are the UK's biggest savings product, with around 22 million people saving almost £79 BILLION in them. Yet with a low Premium Bond rate and the fact for most people all savings are now tax-free – have they lost their lustre? MoneySavingExpert's Martin Lewis uses exclusive statistical analysis to interrogate the big question: Are Premium Bonds worth it?

1. ### What are Premium Bonds?

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.

• Minimum purchase amount: £25 for one-off purchases and monthly standing orders.
• Maximum amount you can hold: £50,000.
• Age limit: Over 16 to buy them; under that age they may be held in the name of under-16s by parents or guardians. Grandparents or great-grandparents can buy then nominate the child's parent or guardian to hold them – this is due to be extended to all adults, but we don't yet know when.

NS&I sexes up the draw by personifying its IT equipment; it calls it Ernie (Electronic Random Number Indicator Equipment). In reality it's a simple, audited, random number generator.

The distribution of prizes changes each month. Below is a table of the typical current distribution:

PRIZE LEVEL NUMBER PER MONTH ODDS OF WINNING AT LEAST THIS AMOUNT PER £1 BOND IN ONE MONTH
£1 million 2 1 in 39,490,368,891
£100,000 5 1 in 11,283,031,922
£50,000 11 1 in 4,387,850,918
£25,000 21 1 in 2,025,162,646
£10,000 51 1 in 877,570,954
£5,000 104 1 in 407,120,538
£1,000 1,843 1 in 38,773,381
£500 5,529 1 in 10,438,988
£100 25,283 1 in 2,404,377
£50 25,283
1 in 1,358,656
£25 3,165,599 1 in 24,500
£0 78,978,153,112 Virtual certainty

Prize breakdown for Feb 2019

• ### Do newer bonds have more chance of winning?

No. This is an urban myth. 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.

• ### How long does it take for bonds to be entered into a prize draw?

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.

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.

2. ### The interest is tax-free – that used to be a big boon, but isn't anymore

Premium Bond prizes (the interest) are paid tax-free. However for most people that's no longer an issue.

On 6 April 2016 the personal savings allowance (PSA) launched. It means all savings interest is automatically paid tax-free and you'll 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 around 95% of people no longer pay tax on their savings – 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).

3. ### The prize rate is 1.4%, but with average luck you won't even earn that

The nearest thing Premium Bonds have to an interest rate is their annual prize rate, which is currently 1.4%. 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 £1.40 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 25 people each had £100 invested, for one to win £25-plus, the remaining 24 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.

#### What'll you win over a year with average luck?

##### NUMBER OF BONDS MEDIAN AVERAGE WINNINGS HOW MANY PEOPLE WIN NOWT £100 Nothing 24 in 25 people win nowt £1,000 Nothing 3 in 5 people win nowt £15,000 £200 1 in 1,552 win nowt £31,000 £400 1 in 3,929,370 win nowt

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.

• ### Why do you have a higher chance at £15,000 than at £31,000?

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. Hence picking £15,000 and £31,000, 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 the 50% mark is likely to be.)

4. ### As NS&I is Government-owned, savings there are as safe as it gets, but these days almost all UK savings are protected anyway

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 – and the maximum you can put in Premium Bonds is £50,000.

• ### In practice though isn't NS&I still safer?

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 Financial Services Compensation Scheme (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, you can wait up to eight days to get your cash out of Premium Bonds.

5. ### Use the unique Premium Bonds Calculator to work out what you're likely to win and whether you're likely to beat savings

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 24,500) 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 PremiumBondCalculator.com.

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.

6. ### If you won't earn over the personal savings allowance, and have average luck, Premium Bonds are unlikely to beat top savings

The personal savings allowance means that basic-rate taxpayers can earn £1,000 of interest a year tax-free (£500 for higher-rate taxpayers).

So that makes the Premium Bond rate very easy to compare with other savings. Let's start by simply using the prize fund rate of 1.4%.

Savings rates have started creeping up recently, though are still far from pre-credit crunch levels. The Premium Bond rate is lower than the top easy-access rate, so your question should be: "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.

#### How Premium Bonds compare with other savings over a year

TABLE_CELL_STYLE £1,000 SAVED £5,000 SAVED £20,000 SAVED
Premium Bonds (1) £14 £70 £280
Top savings £15.50 £77.50 £310
Top easy-access ISA £14.50 £72.50 £290
Two-year fixed savings £23.10 £115.50 £462
Two-year fixed ISA £19 £95 £380
Tesco Bank £30 £148 (2) £177.60 (2)
Nationwide FlexDirect (3) £50 £244.50 (4) £244.50 (4)
(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. (2) Interest can't compound above this value so the gross rate is used. You can have two of these accounts, so can earn 3% AER on £6,000. (3) Interest earned in the first year. (4) You can have two of these accounts (one must be joint) so can earn 5% for a year on £5,000.

As you can see, Premium Bonds can still be beaten even by the current low savings rates, and that's when I exaggerate what they're 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 1.4% prize rate, so let's compare the predicted returns using the Premium Bond Probability Calculator.

#### Chance of beating a 1.55% savings account if you don't pay tax on interest

£100 £1,000 AMOUNT OF BONDS INTEREST EARNED IN A TOP SAVINGS ACCOUNT INTEREST AT 1.55% (1) WHAT % CHANCE PREMIUM BONDS HAVE OF BEATING TOP SAVINGS Over one year £1.55 5% £15.50 39% £77.50 25% £465 23% £775 17% (1) Top savings account paying 1.55% interest, it assumes the interest 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.

So, when we compare Premium Bonds against simple top standard savings, you're actually more likely to win with savings than Premium Bonds, if you have average luck.

Now let's compare to the top bank account savings – so the amount of interest you'd get if you make every penny work for you in the best possible account – here Premium Bonds fare even worse...

With £5,000 in two Nationwide FlexDirect accounts you'd earn £244.50 in interest in the first year; the chances of Premium Bonds beating that is around 1 in 146.

Keep £6,000 in two Tesco Bank accounts and you'd earn £177.60/year in interest – the chances of Premium Bonds beating that is around 1 in 39.

Of course these are complex accounts with criteria to meet to earn interest (see Best Bank Accounts), but max them out – assuming average luck – they'll almost always spank Premium Bonds' bottom.

So overall the summary is, Premium Bonds can beat normal easy-access savings, but you'll need to have above average luck to ensure that comes true – and for many, the savings will still win. If you're saving in high-interest bank accounts, those will almost always win.

7. ### If you will earn over the personal savings allowance, and have average luck, Premium Bonds become a far better bet

Premium Bonds come into their own for those with larger amounts of savings, especially if you're a higher- or top-rate taxpayer. This is because if you've used up your personal savings allowance (PSA) on normal savings – so you earn over £1,000 of interest a year as a basic-rate taxpayer or over £500 for higher-rate taxpayers – then all savings above that are taxed at your income tax rate.

That means a basic-rate taxpayer only gets 80% of their interest, a higher-rate 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 PSA, so it's almost like an extra allowance.

Let's start by simply using the Premium Bond prize fund rate of 1.4% – even though as explained already most people won't win that much.

#### How Premium Bonds compare with other savings rates if you pay tax on your interest

##### AMOUNT SAVED WITHIN PSA/NON-TAXPAYER BASIC-RATE TAX HIGHER-RATE TAX TOP-RATE TAX Premium Bonds (1) 1.4% 1.4% 1.4% 1.4% Top savings 1.55% 1.24% 0.93% 0.85% Top easy-access ISA 1.45% 1.45% 1.45% 1.45% Two-year fixed savings 2.31% 1.85% 1.39% 1.27% Two-year fixed ISA 1.9% 1.9% 1.9% 1.9% Tesco Bank 3% 2.4% 1.8% 1.65% Nationwide FlexDirect 5% 4% 3% 2.75% (1) Someone with average luck is actually likely to win less than this.

Now let's take the analysis up a step, and look at how likely you are to beat top savings with Premium Bonds.

#### Chance of beating a 1.55% savings account over a year if you pay tax

£100 £1,000 £5,000 £30,000 £50,000 AMOUNT OF BONDS ODDS OF WINNING £0 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 95% chance £1.24 5% £0.93 5% 61% chance £12.40 39% £9.30 39% 9% chance £62 45% £46.50 71% 1 in 2,407,703 £372 56% £279 82% Negligible £620 56% £465 91%

So overall, the higher the rate you pay tax, and the more money you are saving in Premium Bonds, the better a bet they look for you.

Yet that's against the weakest competition, simple top standard savings – against the top bank account savings, Premium Bonds' advantage is nowhere near as strong...

With £5,000 in two Nationwide FlexDirect accounts after basic 20% tax you'd earn £195.60 in interest in the first year; the chances of Premium Bonds beating that is around 1 in 70.

As we've said, it's a complex account (see Best Bank Accounts) but for those with a few thousand saved, it'll usually beat Premium Bonds, so you'd probably want to consider filling it up first.

So overall the summary is, if you will earn over the PSA, then Premium Bonds are an option you could look at, though with average luck there are still a range of savings that pay more.

8. ### Of course you may have better than average luck, but don't bank too hard on winning the jackpot...

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 39 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.

9. ### The most powerful psychological sell of Premium Bonds is that interest is called winning

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 £100+ a year – that's £25 every few months. The same money in Tesco savings would "win" £178 a year, guaranteed.

Normally in finance there's a risk premium: you should expect higher returns when there's a higher risk. For some perverse reason, with Premium Bonds, people tend to be happy to earn less when there's a risk.

Even if we go with that, don't just rely on your memory of what you won. 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.

10. ### Premium Bonds are unlikely to beat inflation at the current rate

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.

Sadly many savings accounts don't beat inflation, especially now inflation's on the rise again. I thought it'd be useful to show you how Premium Bonds are likely to play out against it.

#### Chance of beating inflation (CPI at 2.1%)

AMOUNT OF BONDS AMOUNT NEEDED TO BEAT INFLATION ODDS OF EARNING THIS OR MORE WITH PREMIUM BONDS
Over one year
£100 £2.10 5%
£1,000 £21 39%
£5,000 £105 12%
£30,000 £630 4%
£50,000 £1,050 5%
11. ### You can opt to resave your winnings, so the gain compounds (hopefully)

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.

12. ### There is more than £61 million in unclaimed Premium Bonds prizes, it only takes a few minutes to check if you're owed…

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.

Among the unclaimed prizes is more than £8 million-worth that has been lost in the post – see our news story for more.

13. ### Premium Bonds can't be passed on if you die, but what they're worth will be

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). Plus, with NS&I, you may need to get probate on the estate, if the 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.

14. ### A final thought: are Premium Bonds worth it?

Look at Premium Bonds with a clinical financial eye and they're only a good bet as a serious place to put savings if you're lucky, or you're a higher- or top-rate taxpayer who has used up their personal savings allowance, cash ISA allocation, and top bank savings accounts.

Even though many rates have dropped, the top bank savings accounts will all still smash the pants off Premium Bonds, unless you've extremely good luck. And even the top cash ISAs and normal savings are usually likely to pay higher returns, even though their interest rates are actually lower than the Premium Bonds rate, it's a lucky person who'll actually break even with that rate on Premium Bonds.

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 1.4% 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 quite a lot less than 1.4%, 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.