Premium Bonds — the maths behind the prize draw

Premium Bonds are the UK’s strangest savings product. You don’t earn interest — you enter a monthly prize draw. The maths is genuinely different from a normal savings account, and most coverage of Premium Bonds undersells just how different. This is the working.

How the prize draw works

Each £1 Premium Bond is a separate entry in a monthly prize draw. Holders are eligible from the first calendar month after their bond is purchased.

• The prize fund rate is the percentage of the total bond holding that NS&I pays out in prizes each year. Currently it’s around 3.8% (it’s changed several times in recent years as interest rates have moved).
• Prizes range from £25 to £1,000,000. Two £1m prizes are awarded each month.
• The minimum holding is £25; the maximum is £50,000.
• Prizes are tax-free and don’t need to be declared on Self Assessment.

The headline rate (3.8% in this example) is the expected payout across all bondholders combined. Your individual return depends on whether you win prizes — and the distribution is heavily skewed.

NS&I’s Premium Bonds page →

What “3.8%” doesn’t mean for an individual holder

Three crucial points the headline figure hides:

1. The median holder earns less than the headline rate

The prize fund is dominated by a few large prizes (the £1m and £100,000 awards skew the average up). A holder with £10,000 of bonds, in any given year, is more likely to earn somewhere around 3.0–3.5% than the headline 3.8% — because the high-value prizes are unlikely to land in their bonds.

NS&I publishes a “prize checker” tool and odds:

• Odds of any one bond winning a prize in a single draw: roughly 22,000 to 1.
• Most prizes are £25 or £50: the vast majority of winners receive small amounts.
• The £1m prize: roughly 1 in 60 million per bond per draw. For someone holding the maximum £50,000, that’s a 1 in 1,200 monthly chance of winning the jackpot — over a year, about 1%.

2. Variance is high for small holders

A holder with £100 of bonds might go years without winning anything. A holder with £50,000 is much more likely to win something each month, but the rate they earn varies materially year-on-year.

A rough rule from public NS&I data: with the maximum £50,000 held, you can expect to win roughly the prize rate on average over several years — but in any single year you might earn 1% or 5%. The variance smooths out only over long periods or very large holdings.

3. There’s no compounding

Unlike an interest-bearing account, prizes don’t add to your bond holding automatically (unless you opt in to bond reinvestment). Without reinvestment, your bond holding stays static and the headline rate doesn’t compound — which makes the comparison to a compounding savings account flatter the bonds slightly.

When Premium Bonds make sense

Three situations where they’re a reasonable choice:

1. You have cash above the FSCS £85,000 limit

NS&I products are 100% backed by HM Treasury. There’s no £85,000 cap on the protection. For someone holding £200,000 in cash who doesn’t want to split across three FSCS-protected banks, Premium Bonds (up to £50,000) plus an NS&I Direct Saver can sit unprotected by the standard scheme but still government-backed.

2. You’re a higher-rate or additional-rate taxpayer with PSA filled

Higher-rate taxpayers get a £500 Personal Savings Allowance; additional-rate get £0. Above the PSA, interest on cash savings is taxable. Premium Bonds prizes are tax-free, so the effective return is the headline rate, not the headline rate minus 40%.

The break-even depends on your tax band:

• Basic rate (20%): a 4.5% taxable savings account earns 3.6% after tax. Premium Bonds at 3.8% headline is roughly equivalent.
• Higher rate (40%): a 4.5% taxable account earns 2.7% after tax. Premium Bonds at 3.8% wins by a meaningful margin.
• Additional rate (45%): 4.5% becomes 2.475% after tax. Premium Bonds wins by more.

3. You enjoy the prize-draw element

This is a behavioural argument, not a financial one — but a real one. Some people find Premium Bonds psychologically more rewarding than watching interest accrue, and that’s a reason to keep some money there even when the maths is marginal.

When Premium Bonds don’t make sense

A few situations where the alternative is clearly better:

• You’re a basic-rate taxpayer with PSA headroom. A 4.5% easy-access savings account beats 3.8% Premium Bonds after tax, and pays predictably.
• You haven’t filled your ISA allowance. A cash ISA at the same headline rate as Premium Bonds is tax-free anyway, but pays predictably and compounds.
• You need the cash for a specific date. Premium Bonds have no guaranteed return in any given month. For known upcoming expenses, fixed-rate bonds or a savings account is more reliable.
• You’re hoping for the £1m prize. The probability isn’t zero, but it’s low enough that planning around it is unwise. The expected value is roughly the prize fund rate.

A reasonable role for Premium Bonds

For most savers, Premium Bonds fit best as:

• A portion of cash savings above ISA allowance and PSA — particularly for higher-rate taxpayers.
• A safety net for money above the FSCS limit when you don’t want to split across banks.
• A small allocation kept “just for fun” if the prize draw element matters to you.

The maths typically doesn’t support putting the whole emergency fund in Premium Bonds — the variance is too high. A cash ISA paying close to the prize rate is more predictable.

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Last updated 22 May 2026. The Premium Bonds prize rate changes from time to time — check the NS&I current rates page for today’s figure. This guide is educational and is not personal financial advice. See our disclaimer.