Premium Bonds Median Returns Analysis: What You'll Really Win
NS&I's advertised 3.6% prize fund rate is a mean average—but what do typical Premium Bonds holders actually win? Our Monte Carlo analysis of 10,000 simulations reveals that median returns are significantly lower, particularly for smaller holdings.
📊 Key Finding
The median annual return for Premium Bonds holders is substantially below the 3.6% prize fund rate. A holder with £50,000 typically receives around 3.25%, while someone with £1,000 has a median return of zero—they're more likely to win nothing than something over 12 months.
Why Mean and Median Differ
When NS&I states the prize fund rate is 3.6%, this is the mean (arithmetic average) return across all bondholders. However, this figure is heavily skewed by rare large prizes—particularly the two £1 million jackpots awarded each month.
To illustrate: imagine a lottery where one person wins £1 million and 999,999 people win nothing. The "average" payout is £1 per person—technically accurate, but deeply misleading about what a typical participant experiences. Premium Bonds work similarly, though less extremely.
The median return—the point where half of holders earn more and half earn less—provides a far more realistic picture of typical outcomes. Our analysis uses Monte Carlo simulation to calculate these median returns at various holding levels.
Median vs Mean Returns by Holding Amount
The following table shows expected annual returns based on 10,000 Monte Carlo simulations per holding level, using the current prize fund rate of 3.6% and odds of 1 in 22,000 per £1 bond per month.
| Holdings | Mean Return | Mean % | Median Return | Median % | Probability of £0 |
|---|---|---|---|---|---|
| £500 | £18 | 3.60% | £0 | 0.00% | 76% |
| £1,000 | £36 | 3.60% | £0 | 0.00% | 58% |
| £2,000 | £72 | 3.60% | £25 | 1.25% | 34% |
| £5,000 | £180 | 3.60% | £125 | 2.50% | 10% |
| £10,000 | £360 | 3.60% | £275 | 2.75% | 3% |
| £20,000 | £720 | 3.60% | £600 | 3.00% | <1% |
| £30,000 | £1,080 | 3.60% | £950 | 3.17% | <0.5% |
| £50,000 | £1,800 | 3.60% | £1,625 | 3.25% | <0.1% |
Data: Monte Carlo simulation (10,000 iterations per holding level). Prize fund rate: 3.6%. Odds: 1 in 22,000. Analysis date: January 2025.
The Scale Problem
The data reveals a stark reality: Premium Bonds have a significant scale problem. Holders with smaller amounts face a high probability of receiving nothing whatsoever over a 12-month period.
This creates an unusual dynamic: Premium Bonds work best for wealthy savers who can hold close to the £50,000 maximum. At this level, median returns (3.25%) approach the mean (3.6%), and the tax-free nature provides genuine value—especially for higher-rate taxpayers.
Conversely, the 63% of holders with under £500 invested are statistically likely to win nothing in any given year while foregoing guaranteed returns available in savings accounts or Cash ISAs.
Methodology: Monte Carlo Simulation
Our analysis uses Monte Carlo simulation—a statistical technique that models random outcomes by running thousands of simulated scenarios. This approach is more accurate than simplified mathematical formulas because it accounts for the discrete prize structure and variance inherent in Premium Bonds.
How the Simulation Works
For each holding amount, we run 10,000 independent simulations of a 12-month period. Each simulation:
- Calculates expected wins: Using Poisson distribution with λ = (bonds × odds per bond × 12 months), where odds per bond = 1/22,000.
- Assigns prize values: For each win, a prize is randomly selected based on the actual NS&I prize distribution (weighted by prize frequency—most wins are £25, fewer are £50, etc.).
- Records total winnings: The sum of all prizes won in that simulation.
After 10,000 simulations, we calculate:
- Mean: The arithmetic average of all simulation outcomes
- Median (P50): The middle value when all outcomes are sorted
- Percentiles: P10 (pessimistic), P90 (optimistic) outcomes
- Probability of £0: Percentage of simulations with no wins
Prize Distribution Used
The simulation uses the actual January 2025 NS&I prize distribution:
| Prize Value | Monthly Prizes | % of Prize Pool |
|---|---|---|
| £1,000,000 | 2 | 0.47% |
| £100,000 | 82 | 1.91% |
| £50,000 | 163 | 1.90% |
| £25,000 | 328 | 1.91% |
| £10,000 | 818 | 1.91% |
| £5,000 | 1,636 | 1.91% |
| £1,000 | 17,163 | 4.00% |
| £500 | 51,489 | 6.00% |
| £100 | 1,987,844 | 46.33% |
| £50 | 1,987,844 | 23.17% |
| £25 | 1,803,871 | 10.51% |
| Total | 5,851,240 | 100% |
Source: NS&I January 2025 prize draw. Total prize fund: £429,090,875. Eligible bonds: 128.7 billion.
Implications for Savers
When Premium Bonds Make Sense
Based on the median return analysis, Premium Bonds are most suitable for:
- Higher-rate (40%) and additional-rate (45%) taxpayers with savings beyond their ISA allowance. Even a 3.25% median return, when tax-free, beats many taxable alternatives.
- Savers who can hold £10,000+ where median returns become more predictable and the gap between mean and median narrows.
- Those who value the excitement of the monthly draw and are comfortable with variance in returns.
When Alternatives Are Better
Premium Bonds may not be optimal for:
- Small savers with under £5,000: The high probability of zero returns means guaranteed interest from savings accounts or Cash ISAs typically provides better outcomes.
- Basic-rate taxpayers with unused Personal Savings Allowance: With £1,000 of tax-free interest available, a 4.5% savings account beats Premium Bonds' 3.25% median return.
- Anyone who hasn't maximised their ISA allowance: Cash ISAs offer guaranteed, tax-free returns without the variance.
🔢 Calculate Your Actual Expected Returns
See your personalised median return, probability distribution, and percentile outcomes based on your specific holding amount.
Frequently Asked Questions
What is the median return on Premium Bonds?
The median return depends on holdings. With £50,000, median annual returns are approximately £1,625 (3.25%). With £10,000, around £275 (2.75%). With £1,000 or less, the median is £0 as most holders win nothing over 12 months.
Why is the median return lower than 3.6%?
The 3.6% prize fund rate is a mean average, skewed upward by rare large prizes including the £1 million jackpot. Since most prizes are £25-£100, and many holders win nothing, the typical (median) return is significantly lower.
How many Premium Bonds do I need for a realistic chance of winning?
With £5,000 invested, you have roughly a 90% chance of winning at least something over 12 months. With £10,000, this rises to about 97%. Below £2,000, the probability of receiving £0 for the entire year is substantial.
Is the Monte Carlo method reliable?
Yes. Monte Carlo simulation is a standard statistical technique used in finance, engineering, and science. With 10,000 iterations, our confidence intervals are narrow and results are reproducible. The method properly accounts for the discrete prize structure and Poisson-distributed win frequency.
Disclaimer: This analysis is for informational purposes only and does not constitute financial advice. Premium Bonds returns are variable and past performance does not guarantee future results. Prize fund rates and odds are subject to change by NS&I. Data accurate as of January 2025. Consider your personal circumstances and consult a financial advisor for personalised guidance.