Premium Bonds: The Maths Says You'll Probably Lose — the Taxman Says You Might Not

Every month, millions of Brits open the NS&I app, tap their bond numbers into the prize checker, and discover — once again — that they have won precisely nothing. It is a ritual as British as queuing and apologising to furniture. And it is costing most of them money.

Premium Bonds are not a savings account. They are a lottery ticket with a government guarantee and a marketing budget. NS&I prefers the word 'prize' to 'interest' for a reason: prizes are exciting, interest is boring, and the distinction lets everyone from the Treasury downwards avoid a very uncomfortable conversation about effective yield.

But here's the contrarian bit. For a specific slice of the British public, Premium Bonds are not just defensible — they are the rational choice. The trick is understanding exactly which slice you're in. Most people have never done the maths.

The odds are not the point (except they absolutely are)

Each £1 bond has a roughly 21,000-to-1 chance of winning a prize in any given month. That sounds remote, and it is. But with enough bonds, the probabilities add up — just not in the way most holders imagine.

Take £10,000 in bonds. You own 10,000 of them. At 21,000-to-1, you'd expect about 0.48 prizes per month, or roughly 5.7 prizes a year. Nice. Except the prize distribution is brutally skewed. Around 90% of prizes are £25, £50 or £100. The £1m and £100,000 jackpots are the shiny objects that keep the whole thing moving.

So while the headline prize fund rate might sit near 3.8% — implying an average return of £380 a year on £10,000 — the median holder gets nowhere near that. A more realistic median outcome for £10,000 is somewhere between £150 and £200 a year. That's an effective yield of 1.5% to 2%. Against a competitive easy-access account paying 3.9%, you are volunteering to be worse off.

The gap between mean and median is the entire story. NS&I advertises the mean. Your bank statement shows the median.

The tax twist that changes everything

Here is where the consensus view starts to wobble. Premium Bond prizes are tax-free. Not 'tax-free up to a personal savings allowance' — actually, permanently, categorically tax-free. No declaration, no form, no nasty letter from HMRC.

For a basic-rate taxpayer, that's worth less than you'd think. The Personal Savings Allowance means you can earn £1,000 of interest outside an ISA before the taxman takes a bite. On £10,000 at 3.9%, you'd earn £390 — comfortably under the limit. Premium Bonds lose here, because even the expected value (£380) is no better than the taxed-nothing easy-access account, and the median is far worse.

For an additional-rate taxpayer, the picture flips. There is no Personal Savings Allowance at 45%. Every penny of interest is taxed at 45%. That same £390 becomes £214.50 after tax. Suddenly the Premium Bond expected value of £380 looks rather good — and the median of £175 is within touching distance of the taxed alternative, with the jackpot upside thrown in.

Scale it up. £50,000 in an easy-access account at 3.9% generates £1,950. An additional-rate taxpayer hands over £877.50, keeping £1,072.50. The same £50,000 in Premium Bonds has an expected return of £1,900, tax-free. The median return on that balance is closer to £1,500 — still comfortably ahead of the taxed savings account. The more bonds you hold, the more the distribution converges on the mean, and the more the tax advantage compounds.

Who actually loses

The losers are not mysterious. They are people with £500 in bonds, wondering why they never win. At £500, you have a 1-in-42 chance of a prize each month. You will go years without a sniff. The median annual return is zero. That is not savings; it is a lottery subscription with a capital guarantee.

The second group of losers are people who haven't used their ISA allowance. The £20,000 annual limit has been frozen since 2017, and if you have unused ISA room, filling it with a competitive cash ISA or a stocks-and-shares ISA is almost always the better move. Premium Bonds are what you do after the tax shelters are full — not instead of them.

The third group is anyone who thinks the headline prize rate is what they'll get. They are the ones who fund the jackpots for everybody else. It is a regressive transfer of expected return from the small saver to the large one, dressed up as a national institution.

And yes, the government gets cheap funding out of it. NS&I is effectively a gilt-edged borrower with a lottery attached. Your daydream is someone else's debt management strategy. But that's not a scandal — it's just the plumbing.

The dream tax is sometimes worth paying

So where does that leave the £100bn-plus sitting in Premium Bonds? Mostly with people who could do better elsewhere, and a meaningful minority who can't. If you are an additional-rate taxpayer with your ISA allowance maxed and a cash buffer you don't want exposed to market risk, Premium Bonds are a perfectly sensible — occasionally even superior — home for part of your savings. The tax-free prize income, the 100% Treasury backing and the instant access add up to a deal that no bank can quite match for that specific profile.

If you are a basic-rate taxpayer with unused ISA allowance and £2,000 in bonds because your grandmother bought them in 1998, you are playing a game you are mathematically destined to lose. Cash them in, stick the money in a competitive easy-access ISA, and sleep just as soundly.

Premium Bonds are not a religion. They are not a scandal. They are a lottery-shaped savings product that suits a narrow set of circumstances and flatters everyone else with a headline number they will never experience. Know your median. Then decide whether the dream is worth the tax.