Are savings going backwards after tax and inflation? Many UK residents wonder whether a high ISA rate or the uncertain prize‑yield from Premium Bonds will deliver better real returns. This guide explains an interactive visualiser designed specifically to compare ISA interest rates and NS&I Premium Bonds prize‑yield, with practical examples and step‑by‑step inputs so readers can see which option suits short, medium or long goals.
Key takeaways: what to know in 1 minute
- ISA interest gives a guaranteed, tax‑free nominal return based on the published rate; use compound frequency to estimate growth.
- Premium Bonds prize‑yield is probabilistic — a headline 'prize‑yield' converts the random prize wins into an annualised expected return but does not guarantee steady cash flow.
- Inflation and tax change relative performance: adjusted real yield matters more than nominal figures when comparing ISAs and Premium Bonds.
- Visualiser shows scenarios where ISAs outperform Premium Bonds (and vice versa) by varying rates, prize‑yield, time horizon and withdrawal frequency.
- Use simple inputs — balance, ISA rate, prize‑yield, time horizon, compounding and prize frequency — to get realistic expected returns.
How the visualiser compares ISA interest and prize‑yield
The visualiser compares two different return mechanics: deterministic interest and probabilistic prizes. For an ISA, the input is a nominal annual interest rate and compounding frequency (daily/monthly/annually). For Premium Bonds, the input is a prize‑yield (expressed as an annual percentage) that represents the expected percentage return across a large population of bonds.
The tool computes, for each option and timeframe, the expected nominal balance and the distribution (for Premium Bonds), then converts results into equivalent annualised returns and inflation‑adjusted real yields. Key outputs are: expected end balance, annualised internal rate of return (IRR), and probability percentiles for Premium Bonds wins (e.g. median, 90th percentile).
How prize‑yield is defined in the visualiser
Prize‑yield here means the expected annual return rate derived from the distribution of prizes NS&I publishes. It is not an interest rate — rather a statistical expected value per £1,000 held. The visualiser uses the declared NS&I prize‑yield figure (or a custom value) and treats it as the mean of a Poisson/Binomial win process to model the probability of winning any prize each monthly draw.
How ISA interest is modelled
ISA interest is modelled as a nominal annual rate with the chosen compounding frequency. Interest credited is tax‑free. The visualiser applies standard compound interest formulas to compute balances and effective annual rate (EAR):
- Effective annual rate (EAR) = (1 + r / n)^(n) - 1
where r = nominal annual rate, n = compounding periods per year.
Calculate expected returns: ISA rates versus Premium Bonds
When comparing, two calculations run in parallel.
1) ISA deterministic projection: growth(t) = principal * (1 + EAR)^{t}.
2) Premium Bonds expected projection: expected_growth(t) = principal * (1 + prize_yield)^{t}, but the visualiser also models variance: the distribution of outcomes around the expectation, since actual returns are discrete prizes and can be zero in many periods.
Example calculation (illustrative, current at time of writing)
Assume £10,000 initial holding, 5 years horizon. Inputs: ISA 4.0% AER compounded monthly; Premium Bonds prize‑yield 2.6%.
- ISA EAR ≈ (1 + 0.04/12)^{12} - 1 = 4.07%
- ISA 5‑year expected balance ≈ £10,000 * (1.0407)^{5} ≈ £12,214
- Premium Bonds expected balance ≈ £10,000 * (1.026)^{5} ≈ £11,357
This simple deterministic comparison suggests the ISA outperforms in expectation. The visualiser adds the win‑distribution for Premium Bonds showing a high probability of outcomes below the expectation and a long tail of large wins; it reports median and percentile outcomes.
When to use expected value vs distribution
For wealth planning, expected value is useful for mean outcomes; for cash‑flow planning or emergency funds, the distribution (probability of zero wins or large jackpots) matters more. The visualiser provides both a mean expected return and percentile outcomes to address both concerns.
Understanding NS&I Premium Bonds and ISA tax‑free returns
Premium Bonds are issued by NS&I and offer prizes instead of interest. Winnings are tax‑free and monthly draws determine prizes. An ISA provides interest that is tax‑free within the ISA wrapper. Both have no income tax on returns — but mechanics differ and so do risk/variability profiles.
Tax treatment comparison
Both Premium Bonds and Cash ISAs produce tax‑free returns for individuals in the UK. This removes income tax from the comparison — the focus should therefore be on pre‑tax expected real returns and the cash‑flow variability of Premium Bonds.
Liquidity and access
- Cash ISAs generally allow easy withdrawals depending on provider terms; some fixed‑rate ISAs impose exit penalties.
- Premium Bonds are highly liquid through NS&I online or phone redemption, with funds typically available within a few working days.
Real returns = nominal return - inflation (approx) or use (1 + nominal)/(1 + inflation) - 1 for accuracy. The visualiser allows the user to set an inflation rate (CPI or RPI) and see real expected performance.
Why inflation adjustment matters
Two savings options with identical nominal returns can differ materially in purchasing power over time. For example, a 4% ISA against 3% inflation yields roughly 1% real; a 2.6% prize‑yield under the same inflation is negative in real terms.
Visualiser outputs for inflation
- Real expected annualised yield for each option.
- Time series chart of purchasing power (balance adjusted to today’s prices).
- Sensitivity analysis: change inflation plus/minus 1% to observe breakpoints where Premium Bonds might look preferable.
The visualiser includes scenario presets to highlight typical cases where ISAs win or lose vs Premium Bonds.
Scenario A — higher ISA fixed rate
- ISA rate 4.5% vs Premium Bonds prize‑yield 2.6%. Over most horizons longer than one year, ISA outperforms in expected balance and lower variance. The visualiser displays the crossing point (time when cumulative expected gap exceeds a chosen threshold, e.g. £500).
Scenario B — short horizon and chance of jackpot
- For a 6–12 month horizon and low ISA rates (e.g. 1.0%), the Premium Bonds long tail could, by chance, deliver a large lump sum. The visualiser shows probability of getting a prize above a given threshold (e.g. £5,000) which, while small, drives some savers' preference.
Scenario C — inflation spike
- If inflation rises rapidly and ISA rates lag, both nominal options may lose real purchasing power. The visualiser flags negative real yields and suggests caution for long‑term capital preservation.
This section mirrors the tool’s input panel and explains the effect of each field.
- Initial balance (e.g. £10,000).
- Time horizon (months or years).
- ISA nominal rate (AER or nominal).
- ISA compounding frequency (monthly, annual, daily).
- Premium Bonds prize‑yield (use NS&I official or custom).
- Prize draw frequency (monthly — NS&I does monthly draws).
- Expected inflation (annual %).
How to choose realistic frequencies
- For ISA compounding, monthly and annual are the most common. Choose the provider’s stated compounding to match reality.
- Premium Bonds prize draws are monthly by design; the visualiser simulates monthly Bernoulli processes for wins.
1) Enter £10,000 initial balance.
2) Set horizon to 5 years.
3) ISA rate 4.0% AER, monthly compounding.
4) Premium Bonds prize‑yield 2.6% (NS&I published), monthly draws.
5) Inflation 3.0%.
Interpretation: The visualiser will show nominal and real expected balances, distribution percentiles for Premium Bonds, and give the user plain English verdicts such as "ISA expected to deliver higher median and mean balances; Premium Bonds have low probability of large one‑off wins." These statements are accompanied by charts and downloadable CSV data.
| Feature |
Cash ISA |
Premium Bonds |
| Typical return profile |
Guaranteed nominal interest (AER) |
Random prizes; expected prize‑yield is statistical |
| Tax treatment |
Tax‑free within ISA wrapper |
All prizes tax‑free |
| Liquidity |
Generally easy; fixed ISAs may restrict withdrawals |
High liquidity via NS&I redeem |
Visualiser process: compare and decide
🔢 Step 1 → Enter balance, horizon and ISA rate.
🎯 Step 2 → Enter Premium Bonds prize‑yield and choose inflation.
📊 Step 3 → View expected balances, percentile distribution and real yields.
✅ Step 4 → Download CSV or run scenario sensitivity (+/− 1% inflation, rate shocks).
Advantages, risks and common mistakes
✅ Benefits / when to apply
- Choose a Cash ISA when a comparable or higher guaranteed AER is available than the expected prize‑yield and the priority is predictability.
- Choose Premium Bonds if the saver values the chance of a tax‑free lump sum and accepts variability; suitable for lottery‑style upside or emergency fund for those who accept low median returns.
- Use the visualiser to test multiple horizons and inflation scenarios before committing.
⚠️ Errors to avoid / risks
- Ignoring inflation: comparing nominal ISA AER to nominal prize‑yield without adjusting for inflation can mislead.
- Confusing prize‑yield with guaranteed interest: prize‑yield is an expected value, not a guaranteed rate.
- Using short horizons for average expectations: Premium Bonds mean expected value converges over large populations and time; for a single holder over short horizons, variance dominates.
Frequently asked questions
What is prize‑yield and how does it relate to chance of winning?
Prize‑yield is the expected annual return across all bondholders based on NS&I prize distribution. It translates the odds into an average percentage but does not predict whether any individual will win.
How does compounding differ between ISAs and Premium Bonds?
ISAs compound at the stated frequency (monthly, annual). Premium Bonds do not compound in the traditional sense; winnings can be reinvested to create compounding, but actual compounding depends on reinvestment behaviour.
Can the visualiser use the official NS&I prize‑yield automatically?
Yes. The visualiser fetches the latest published prize‑yield from NS&I when online, or allows manual entry.
Is interest from ISAs and Premium Bonds tax‑free?
Yes. Interest within an ISA and Premium Bonds prizes are tax‑free for UK residents.
Which is better for an emergency fund?
A Cash ISA with instant access is usually better due to predictable returns. Premium Bonds are liquid but return variability makes them less reliable for planned short‑term needs.
How should inflation be set in the visualiser?
Use recent CPI figures as a baseline; try sensitivity of ±1% to understand breakpoints. Official inflation series are available at ONS.
Your next step: practical actions to take today
- Enter current balance and horizon into the visualiser and compare expected vs median outcomes.
- Run two sensitivity tests: inflation +1% and ISA rate −0.5% to see robustness.
- Download the scenario CSV and save the result for reference when choosing between ISA and Premium Bonds.