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Cash ISA 2027 Cap Impact Calculator
Calculate the long-term wealth loss of the new £12,000 Cash ISA cap for under-65s compared to the legacy £20,000 limit.
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Guide & How-To
Calculate what you can realistically expect to win from UK NS&I Premium Bonds. Unlike a savings account with a guaranteed interest rate, Premium Bonds offer a variable return based on luck. This calculator shows your expected (mean) return, your more realistic median return based on your holding size, the odds of winning nothing, and the inflation-adjusted purchasing power of your prizes. All figures use the current 3.80% prize fund rate (effective July 2026 draw) with 22,000-to-1 odds.
How Premium Bonds Work: Prize Fund Rate vs Your Actual Return?
Premium Bonds are a UK government-backed savings product from NS&I where, instead of earning interest, each £1 bond is entered into a monthly prize draw. The headline 'prize fund rate' of 3.80% is the average return across all bondholders — not a guaranteed return for you. Because the prize distribution is highly skewed (two £1 million jackpots consume a disproportionate share of the prize fund), most bondholders earn significantly less than the headline rate. A £50,000 holder has a median return of approximately 3.3%, while a £10,000 holder has a median closer to 3.0%. Smaller holdings under £1,250 typically win nothing in a year.
The Odds: Understanding Your Winning Probability?
Each £1 Premium Bond has a 22,000-to-1 chance of winning any prize in each monthly draw. This means with £10,000 invested, you would statistically expect about 5.5 prizes per year, but the actual number could be higher or lower. The probability of winning nothing at all over a given period decreases as your holding increases. With £50,000 (the maximum), you are virtually guaranteed to win multiple prizes every year. With £1,000, you have roughly a 58% chance of winning nothing over a full year. Despite the lottery element, your capital is always 100% secure, backed by HM Treasury.
Premium Bonds Expected Return & Odds
Premium Bonds are a unique UK government-backed savings product where each £1 bond is entered into a monthly prize draw instead of earning interest. Unlike a fixed-rate savings account, the return is not guaranteed — it depends entirely on random draws conducted by ERNIE, NS&I's random number generator. The expected (mean) return is straightforward: multiply your investment by the prize fund rate and the time held. However, because the prize distribution is heavily skewed by two £1 million jackpots each month, the median return is significantly lower than the mean for most holders.
The probability of winning nothing follows a binomial distribution: each £1 bond has a fixed survival probability (21999/22000) each month. Over thousands of bond-months, this compounds into the overall chance of receiving zero prizes. The expected number of prizes per year equals your total investment divided by the odds (22,000). For a £10,000 holder, this means approximately 5.5 prizes per year on average — but in any given year, you might win 3, 8, or even 0.
The median return approximation accounts for the skewed prize distribution. For holdings with fewer than one expected prize per year, the median is effectively zero (most small holders win nothing). For larger holdings, the median approaches the mean as the law of large numbers stabilizes returns. A £50,000 holder (expecting ~27 prizes/year) has a median very close to the headline 3.80% rate, while a £5,000 holder (expecting ~2.7 prizes/year) has a median around 2.8%.
Calculation Steps:
- Determine your investment amount (I) between £25 and £50,000. This is the total number of £1 bonds you hold, each with a unique number entered into every monthly draw.
- Determine your holding period in months (M). Premium Bonds are held continuously; each bond is entered into every draw until cashed in.
- Calculate the expected (mean) annual return: Expected Return = I × r × t where r is the prize fund rate (default 3.80%) and t is the time in years. This represents the average return across all bondholders.
- Calculate the probability of winning nothing: P(zero) = (1 - 1/22,000)^(I × M). For each bond each month, there is a 21,999/22,000 chance of not winning. Over I bonds held for M months, this compounds.
- Calculate the expected number of annual prizes: N_p = I × 12 / 22,000. This helps determine how stable your returns are likely to be.
- If N_p < 1, the median return is effectively £0 — most holders at this level win nothing in a year. If N_p >= 1, estimate the median return using: Median = E × (1 - 0.5 / sqrt(N_p + 1)).
- Calculate the inflation-adjusted (real) return using the Fisher equation: Real Rate = (1 + r) / (1 + i) - 1, where i is the inflation rate. Apply this real rate to your investment to see the purchasing power of your expected winnings.
- Compare the median return rate against alternative savings products. A top easy-access Cash ISA at 4.5% guaranteed will typically outperform Premium Bonds for most holders, especially basic-rate taxpayers.
Real-World Worked Example
Step 1: An investor puts £10,000 into Premium Bonds for 12 months at the current 3.80% prize fund rate with 22,000-to-1 odds. Inflation is assumed at 2.5%.
Step 2: Expected (mean) annual return = £10,000 × 0.038 × 1 = £380. This is the headline figure NS&I advertises, but very few individual holders actually receive exactly this amount.
Step 3: Expected annual prizes = £10,000 × 12 / 22,000 = 5.45 prizes per year. This means statistically you'd expect around 5 or 6 prizes annually, though actual results vary.
Step 4: Probability of winning nothing over the full year = (21,999/22,000)^(10,000 × 12) ≈ e^(-120,000/22,000) ≈ 0.43%. This means a £10,000 holder has a 99.57% chance of winning at least one prize in a year.
Step 5: Median return = £380 × (1 - 0.5 / sqrt(5.45 + 1)) = £380 × 0.803 = £305. This means a typical £10,000 holder with average luck would win approximately £305 in prizes annually — an effective median rate of 3.05%.
Step 6: Inflation-adjusted return = £10,000 × ((1.038 / 1.025) - 1) × 1 = £10,000 × 0.01268 = £126.80. After accounting for 2.5% inflation, the real purchasing power gain from the expected return is just £126.80.
Step 7: Compare against a Cash ISA at 4.5%. The guaranteed ISA return would be £450, which is £145 more than the median Premium Bonds return of £305. However, for a higher-rate taxpayer with no remaining PSA, the ISA return is also tax-free and the comparison becomes purely about the guaranteed vs lottery-based return.
In-Depth Financial Analysis
Premium Bonds are issued by National Savings and Investments (NS&I), an executive agency of HM Treasury. Unlike conventional savings accounts that pay a guaranteed interest rate, Premium Bonds operate on a prize draw model. Each £1 bond is assigned a unique number, and all bond numbers are entered into a monthly draw conducted by ERNIE (Electronic Random Number Indicator Equipment). Prizes range from £25 to £1 million, and all prizes are completely tax-free.
The prize fund is calculated as one month's interest on the total value of all eligible bonds at the published annual prize fund rate. For the July 2026 draw, this rate is 3.80%, with approximately £399 million distributed across 6,049,850 prizes each month. The odds of each individual £1 bond winning any prize in a given month are 22,000 to 1.
The distribution of prizes is intentionally skewed to create large headline jackpots. 80% of the prize fund goes to low-value prizes (£25, £50, £100), 10% to medium-value prizes (£500, £1,000), and 10% to high-value prizes (£5,000 to £1 million). This means that while the mathematical expected return is 3.80%, most individual holders receive significantly less. The two monthly £1 million jackpots alone consume approximately 0.5% of the prize fund but represent an outsized share of the 'expected return' calculation.
For practical financial planning, the median return is more relevant than the mean. Research shows that a £50,000 holder (the maximum) has a median annual return of approximately 3.3% (£1,650), converging towards the headline rate as holding size increases. A typical £10,000 holder has a median around 3.0% (£300), while holders with less than £1,250 are more likely to win nothing than to receive any prize in a typical year.
Premium Bonds are most suitable for: (1) higher-rate and additional-rate taxpayers who have exhausted their £20,000 ISA allowance and their Personal Savings Allowance; (2) those who prioritize capital security (100% HM Treasury backed) over yield; and (3) savers who enjoy the 'lottery thrill' of potentially winning a life-changing sum.
They are least suitable for: (1) basic-rate taxpayers with unused ISA allowance who can get a higher guaranteed return; (2) those needing predictable regular income; and (3) small savers with limited capital who would likely win nothing for extended periods.
Legal & Regulatory Guidelines (2026)
Premium Bonds are not covered by the Financial Services Compensation Scheme (FSCS) because they are 100% backed by HM Treasury — the UK government guarantees every pound invested, making them the safest possible home for UK savings with no upper limit on the guarantee.
NS&I is an executive agency of HM Treasury, operating under the National Debt Act 1972 and the National Savings Bank Act 1971. The prize fund rate and odds are set by NS&I in response to market conditions, the Bank of England base rate, and the government's Net Financing target.
All Premium Bonds prizes are exempt from UK Income Tax and Capital Gains Tax under the Income Tax (Trading and Other Income) Act 2005 (ITTOIA 2005), Section 691. This tax-free status applies regardless of the prize amount or the holder's tax bracket.
Under the FCA's Consumer Duty rules (effective July 2023), NS&I must ensure that Premium Bonds are distributed to appropriate customers and that marketing materials clearly communicate the variance of returns, not just the headline prize fund rate.
Key Strategic Takeaways
- The headline 3.80% prize fund rate is NOT your guaranteed return — it's the average across all bondholders. Your actual return depends on luck.:
- The more Premium Bonds you hold and the longer you hold them, the closer your personal return converges to the headline rate due to the law of large numbers.:
- Premium Bonds are strictly worse than a top Cash ISA for most basic-rate taxpayers who have not exhausted their £20,000 ISA allowance.:
- For higher-rate (40%) taxpayers who have used their ISA allowance, Premium Bonds become competitive because all prizes are tax-free, unlike savings account interest which faces the 40% marginal rate.:
- With inflation at 2.5%, the real (inflation-adjusted) return on Premium Bonds is barely positive for most holders, meaning your purchasing power may not grow significantly.:
- Premium Bonds should not be your primary emergency fund if you need predictable access to interest income — a standard easy-access savings account is better for this purpose.:
Common Pitfalls to Avoid
- Confusing the prize fund rate with a guaranteed interest rate. The 3.80% is a statistical average, not a promised return on your specific investment.
- Assuming that Premium Bonds are 'better' than a Cash ISA because all prizes are tax-free. For most basic-rate taxpayers, a Cash ISA offers a higher guaranteed return with the same tax-free status.
- Overestimating the probability of winning a life-changing jackpot. The odds of winning the £1 million prize in any given month with £10,000 invested are approximately 1 in 6.4 million — comparable to winning the National Lottery.
- Failing to check for unclaimed prizes. NS&I reports tens of millions of pounds in unclaimed Premium Bonds prizes each year. Always keep your address and contact details up to date with NS&I, and use their online prize checker tool.
- Holding Premium Bonds inside an ISA wrapper. You cannot hold Premium Bonds inside an ISA — they are a standalone product with their own tax-free status and £50,000 limit.
Parameters & Input Definitions
Review the glossary of terms used in the calculation model below. Click on highlighted links to read more in-depth definitions in our financial glossary:
| Parameter | Definition & Context |
|---|---|
| Investment Amount | The total amount held in Premium Bonds (£25 minimum, £50,000 maximum). Each £1 is one bond entered into every monthly draw. |
| Holding Period | The number of months you plan to hold the bonds. Longer periods smooth out the random nature of prize draws, with returns converging toward the mean over time. |
| Prize Fund Rate | NS&I's headline annual prize fund rate (currently 3.80% from July 2026). This is the average return across all bondholders, not a guaranteed rate. |
| Inflation Rate | The assumed annual inflation rate used to calculate real (inflation-adjusted) returns. The UK CPI inflation rate is used as the default benchmark. |