How likely is a win on a Premium Bonds holding of £10,000–£100,000? Savers comparing Cash ISAs with Premium Bonds often face vague odds and headline returns rather than clear, comparable figures. Straightforward per‑bond probabilities, prize‑band breakdowns and time‑to‑chance numbers make it possible to judge whether luck or tax relief better serves a specific holding.
Use a Premium Bonds prize‑probability calculator to see your real odds of winning each prize band and the expected annual return on your holding. Enter your stake (e.g. £10k–£100k), choose horizon and reinvestment assumptions, and get per-draw odds, years-to-50% chance, ‑band breakdown and CSV/Excel export to compare directly with ISA or savings accounts.
Premium Bonds prize‑probability and comparison calculator
This tool converts the published NS&I fund rate into a per‑bond, per‑year win probability and lets you compare Premium Bonds with an ISA side‑by‑side. It uses a clear formula and stated assumptions so results (and any approximations) are explicit.
How the per‑bond probability is derived
- Start from the published fund rate r (annual payout per £1). If A is the average prize size across all bands and N is the number of £1 bonds you hold, the expected number of wins per year is
lambda = N × r / A.
- Treating wins as rare, independent events gives a Poisson approximation. The probability of at least one win in T years is
P(≥1 in T) = 1 − exp(−lambda × T).
What the formula assumes and common pitfalls
- Assumes draws are independent and prizes are allocated at random across units; the Poisson approximation is appropriate when the per‑unit win probability is small.
- A frequent error is to present per‑draw probabilities as exact without stating the average prize size A used; A matters because the fund rate is an average payout per £1, not a per‑bond chance.
Practical numeric example
- Example: r = 3.00% (example fund rate), A = £60 (example average prize) and N = 10,000 bonds (£10,000).
Then lambda_year = 10,000 × 0.03 / 60 ≈ 5.0 expected wins per year.
Probability of at least one win in one year = 1 − exp(−5.0) ≈ 99.3% under these assumptions.
What to enter for a fair comparison
- Supply your exact holding (in £1 units), the ISA effective annual rate (EAR), whether ISA interest compounds monthly, whether you reinvest Premium Bonds wins, the time horizon T, and optionally a bespoke fund rate r and average prize size A (the calculator offers a default linked to the latest NS&I figure).
How results are reported and exported
- The tool reports expected annual return, median outcome, 10th/90th percentiles and the probability of at least one win over your horizon. It also shows the number of years to reach an X% chance for Premium Bonds and cumulative interest for the ISA.
- Results for both scenarios can be exported as a CSV so you can open them in Excel, inspect formulas and compare expected returns, medians and percentile outcomes side by side.
Odds by holding size: quick examples for £10k
This section gives direct, numeric examples so the reader sees how odds scale with holdings.
All example figures use the illustrative prize‑fund rate r = 3.00% (2024) and show sensitivity to average prize A.
What are the expected annual returns for these
Expected annual return equals holding × r. Examples:
- £10,000 → £300
- £25,000 → £750
- £50,000 → £1,500
- £100,000 → £3,000 (assuming r = 3.00%)
These figures are the mean expected payout, not guaranteed income.
Example: chance of at least one win in one year
Use lambda_year = N × r / A and P(≥1 year) = 1 − exp(−lambda_year).
With A = £60 and r = 3.00%: £10k → lambda = 5 → P ≈ 99.3%. £25k → lambda = 12.5 → P ≈ 99.9996%.
Sensitivity
If A = £120 (fewer large prizes relative to small ones), odds fall roughly by half.
With A = £120 and r = 3.00%: £10k → lambda = 2.5 → P ≈ 91.8%. £50k → lambda = 12.5 → P ≈ 99.9996%.
Monte carlo simulations and 'years to X%' projections
Monte Carlo simulations show the full distribution of outcomes, not just the mean.
They run thousands of random draws to give median, 10th and 90th percentiles for annual payouts and cumulative wins.
How the simulations work in the calculator
Each run simulates wins per bond using the Poisson or binomial model with the chosen r and A.
The tool repeats this 10,000 times and outputs percentiles and histograms, plus a downloadable run table for Excel.
What percentiles reveal that the mean hides
- The mean equals the prize‑fund rate, but the median can be zero for small holdings and short horizons when the probability of at least one win in the chosen period is below 50%.
- For example, with r = 3.00% and A = £60, a £10,000 holding gives λ ≈ 5 expected wins per year and a one‑year chance of at least one prize of about 99.3%, so the annual median payout for that holding is above zero. This works well in theory, but in practice most holders see no win in any given short period.
- Percentiles reveal the spread of outcomes and show how likely different payout levels are.
Years to reach a target probability
For target probability X of at least one win, solve T = −ln(1 − X) / lambda_year.
Example: for N = 25,000, r = 3.00%, A = £60, lambda_year = 12.5, years to 50% chance T = 0.055 years (about 20 days).
This shows that for moderate holdings, reaching modest probabilities can take surprisingly little time when small prizes dominate.
Premium Bonds are not suitable when the primary goal is guaranteed income or capital access on exact dates. If certainty within weeks matters (for example, a home deposit), a Cash ISA or fixed‑term account is usually preferable.
Visual summary: probability shape and band breakdown
This compact visual clarifies how most payouts are small and large prizes are rare.
It uses three bars to show relative frequency and expected payout share by band.
Prize distribution (illustrative)
Small prizes (e.g. £25): many wins, small share per prize
Mid prizes (e.g. £50–£1,000): fewer wins, larger share each
Top prizes (£100k/£1M): extremely rare but large
It is useful to see how that small per‑bond probability splits across prize bands. Using an illustrative allocation that sums to the total μ = r/A (here 0.0005 per bond per year), typical approximate per‑bond annual probabilities might be: £25 ≈ 0.00040, £50 ≈ 0.00006, £100 ≈ 0.000025, £1,000 ≈ 0.000012, £100,000 ≈ 0.0000008 and £1,000,000 ≈ 0.00000003. For a holding of N bonds you can get expected wins per year by λ_band = N × p_band and the chance of at least one win in that band by 1 − exp(−λ_band). For example, for N = 10,000 (≈ £10,000): expected wins per year ≈ 4 (£25), 0.6 (£50), 0.25 (£100), 0.12 (£1,000), 0.008 (£100k) and 0.0003 (£1M); corresponding per‑year chances are ≈ 98.2% (£25), 45.1% (£50), 22.1% (£100), 11.3% (£1,000), 0.80% (£100k) and 0.03% (£1M).
Scaling to £25k, £50k and £100k gives intuitively larger probabilities (for £25k the £25 band chance is ≈ 99.995%, for £50k the £50 band is ≈ 95.0%, for £100k the £100 band is ≈ 91.8%). These banded odds are illustrative but show why most payouts are small and why very large prizes remain vanishingly unlikely even for substantial holdings.
Common mistakes and clarifications when using the calculator
Many sources equate the mean expected return with a guaranteed interest rate and omit variance.
The calculator makes variance explicit with percentiles and Monte Carlo output so users can see the real spread of outcomes.
What most guides omit when comparing with ISAs
They often ignore that Premium Bonds’ mean equals the prize‑fund rate while the median can be zero.
They also fail to show years‑to‑target probability, which is essential for realistic planning.
Anonymised example of how results
A typical case: a saver with £25,000 assumed r = 3.00% and A = £60.
Expected annual payout = £750, but median one‑year payout was £0 in many Monte Carlo runs; the saver won small prizes intermittently and once won £1,000 in year three.
This example highlights why comparing only means misleads when planning for cash needs.
Use the calculator and export the CSV to compare directly with your chosen ISA rate and horizon.
Frequently asked questions
What are the odds of winning a premium bond prize
Odds depend on the prize‑fund rate and the average prize size.
Enter £50,000 into the calculator with the current NS&I prize‑fund rate to get the exact probability and percentiles.
The tool returns both the chance of any prize and the chance of large prizes for that holding.
How does the calculator treat the NS&I prize‑fund
It uses the prize‑fund rate as the mean payout per £1 per year.
You can use the default current figure or enter a custom rate to run scenarios.
For official figures visit NS&I.
Can I compare Premium Bonds results with a Cash ISA
Yes. The CSV export includes a side‑by‑side sheet for Premium Bonds and the Cash ISA scenario.
It lists yearly expected returns, medians and percentiles so you can inspect formulas in Excel.
This makes a direct apples‑to‑apples comparison simple.
How accurate are the Monte Carlo percentiles
The percentiles are robust when you run 10,000+ simulations and input realistic prize‑fund changes.
They still depend on your assumptions about r and prize distribution over time.
Run sensitivity scenarios with rising or falling prize funds to see a range of possible futures.
Do Premium Bonds beat an ISA after tax? How to compare
Compare the Premium Bonds’ tax‑free expected return to the ISA net of tax in the calculator.
For non‑ISA accounts, adjust interest for your marginal tax rate before comparing.
Remember ISA allowance for 2024/25 is £20,000 and that affects how much you can shelter from tax.
Is it worth moving emergency savings into Premium Bonds
Premium Bonds keep capital safe with the government‑backed guarantee but payouts are uncertain.
If access and predictable interest matter, a Cash ISA or instant access account is usually better.
Use the calculator to quantify how often you would likely see small wins versus guaranteed ISA interest.
Your next step
Try the calculator with your exact holding, set the prize‑fund rate to the current NS&I figure and export the CSV to compare with an ISA rate you trust.
If your situation involves estate planning or large joint‑holder sums, check Premium Bonds Terms & Conditions and consider professional advice.
