How it works
Why compound interest is the only maths that matters for long-term saving
This compound interest calculator is the one UK savers open when they want an honest look at where a pot is heading — with monthly contributions, inflation drag and a tax wrapper applied. Run it next to the percentage calculator, the mortgage calculator and the PAYE salary calculator so you can decide how much of the monthly budget realistically survives for an ISA or workplace pension.
Simple interest grows linearly — a flat fee for lending the bank your money. Compound interest grows exponentially because it pays you interest on the interest. Over 10 or 20 years the gap between the two is enormous, which is why "time in the market" is the most reliable lever a private saver has.
Einstein is often quoted as calling compound interest "the eighth wonder of the world". Whether he did or not, the numbers speak for themselves.
The formula, explained
A = P × (1 + r/n)^(n×t)
- A — the final amount (principal + interest).
- P — the principal, i.e. the starting balance.
- r — the annual interest rate as a decimal (5% → 0.05).
- n — compounding periods per year (annually = 1, monthly = 12, daily = 365).
- t — time in years.
Worked examples
£10,000 at 5% for 10 years, compounded annually
A = 10,000 × (1 + 0.05)^10 = 10,000 × 1.62889 = £16,289
Interest earned = £6,289.
Same sum, compounded monthly
A = 10,000 × (1 + 0.05/12)^(12 × 10) = 10,000 × (1.004167)^120 ≈ £16,470
Monthly compounding adds roughly £181 compared to annual at the same headline rate — a small but free bonus.
Adding £200 a month
Now start with £10,000 and add £200 every month at 5% compounded monthly for 10 years.
Final balance ≈ £47,500 — of which £24,000 is contributions and £13,500 is interest. The habit beats the lump sum.
The rule of 72
A classic mental-maths shortcut: divide 72 by the annual interest rate to estimate how many years it takes for money to double.
| Rate | Approx doubling time | Exact years |
|---|---|---|
| 3% | 24 years | 23.4 |
| 5% | 14.4 years | 14.2 |
| 7% | 10.3 years | 10.2 |
| 10% | 7.2 years | 7.3 |
ISAs: compound interest without the tax drag
In the UK, the Individual Savings Account (ISA) wrapper removes income tax and capital gains tax on the interest and growth you earn inside it. Every adult has an annual allowance (£20,000 for 2025/26), split across Cash, Stocks & Shares, Lifetime and Innovative Finance ISAs.
Over long horizons, protecting gains from tax materially boosts the compounding outcome. A 5% return inside an ISA fully reinvests into the next period; the same 5% return outside, for a higher-rate taxpayer, might lose 40% of the interest to HMRC each year — slashing the effective compound rate.
Things the formula does not capture
- Inflation — A 5% return when inflation is 3% is only a 2% real return. Over 25 years, inflation halves the purchasing power of a pound.
- Fees — Investment platforms, fund charges and advisers skim compound growth. A 1% annual fee over 25 years at 6% gross cuts the final pot by roughly 20%.
- Volatility — Real-world investments don't return a clean percentage each year. Sequencing matters, especially near retirement.
- Tax changes — ISA rules, allowances and dividend taxation have all shifted over the last decade and will again.
Practical savings strategies
- Start early — a £100/month saver who starts at 25 beats a £200/month saver who starts at 45 by retirement age, assuming equal returns.
- Automate contributions — salary-sacrifice pensions and direct debits remove the willpower tax.
- Prioritise employer match — if your employer matches pension contributions, that's an instant 100% return before compounding even starts.
- Use tax wrappers first — ISA allowance and pension allowance are use-it-or-lose-it each year.
AER, APR and gross — why three numbers say the same thing differently
UK savings products advertise rates in a handful of formats, and they are not interchangeable. Knowing which is which stops you comparing apples with pears.
- AER (Annual Equivalent Rate) — the rate you really earn in a year, after all compounding within that year is folded in. Required by the FCA on all savings adverts and the number to compare between accounts.
- Gross rate — the headline annual rate before compounding. An account quoted as 4.9 % gross paid monthly becomes 5.01 % AER.
- APR (Annual Percentage Rate) — a borrowing equivalent; includes product fees and all mandatory charges across the term of a loan. A 4.5 % mortgage with a £999 fee might quote 4.9 % APR.
- Representative APR — the rate that must be offered to at least 51 % of accepted applicants. Your actual rate may be worse depending on credit score.
- AER vs APR gap — AER measures saver benefit, APR measures borrower cost. The same 4 % "rate" on a savings account and on a loan are not the same economic deal because of the fees baked into APR.
Compounding frequency and the continuous-compounding limit
The more often interest is added to the balance, the more the final number grows, but the gains flatten quickly as you speed up. The ultimate limit is continuous compounding, A = P × e^(r×t), which uses the mathematical constant e ≈ 2.71828.
| Compounding frequency | £10,000 at 5 % for 10 years |
|---|---|
| Annual (n=1) | £16,289 |
| Quarterly (n=4) | £16,436 |
| Monthly (n=12) | £16,470 |
| Weekly (n=52) | £16,485 |
| Daily (n=365) | £16,486 |
| Continuous (e^rt) | £16,487 |
Compound interest in reverse — present value and discounting
The same formula, rearranged, tells you how much a future sum is worth today. Flip A = P × (1 + r/n)^(n×t) and solve for P: P = A / (1 + r/n)^(n×t). This is the core idea behind every DCF valuation, pension transfer calculation and mortgage redemption statement.
If you are promised £50,000 in 10 years and your opportunity cost is 5 % a year, the present value is 50,000 / 1.05^10 = £30,696. The further out the payment or the higher the discount rate, the less the future pound is worth today. Lottery jackpots that pay "over 20 years" and defined-benefit pension transfer values are two familiar places the discounting maths shows up.
Myths and common misunderstandings
Compound interest is simple algebra but wrapped in a lot of marketing mythology. Five ideas that regularly trip up UK savers and investors.
- "Banks give you 5 % so savings double in 14 years." — Only if you do not touch the interest. If you spend the interest each year, your balance never grows. Compound maths assumes reinvestment, full stop.
- "Cash is safer than equities in the long run." — Cash is nominally safer but almost always loses to inflation over 10+ years. UK CPI averaged 3.0 % over the last 20 years; a cash ISA paying 2 % would have produced a negative real return.
- "The stock market returns 7 % a year." — It averages around 5 % real globally, before fees and taxes. The "7 %" figure often quoted is the US nominal figure over a very specific window. Always model in real, after-fee terms.
- "Compounding is magic." — It is arithmetic. The reason pensions look small then enormous is that exponentials look flat until they do not. There is no shortcut; time and contribution rate are the only real levers.
- "Starting early makes up for smaller contributions forever." — Only partly. The early saver wins on a given return, but a larger late contribution can close part of the gap if they pick the right product and avoid fees.
Real-world UK compounding journeys
Numbers mean more when a real person carries them. Here are three UK savers at very different stages of life.
Niamh, 22, graduate, £200 a month into a Stocks & Shares LISA
Niamh invests £200 a month into a Lifetime ISA with a global equity tracker. The government adds a 25 % bonus on every contribution, effectively £250 a month invested at a long-run 5 % real return. Over 38 years to age 60, the pot reaches roughly £278,000 in today's money — of which £91,200 is her own money and £22,800 the government's bonus. Compounding does the rest.
Ravi and Priya, 35, saving for a 10-year house upgrade
They deposit £20,000 and save £400 a month in a Cash ISA at 4.5 % AER. After 10 years, the pot is £91,700, of which £20,000 is the initial deposit, £48,000 is ongoing deposits and £23,700 is interest. At current rates that is a noticeable chunk of a stamp-duty-plus-deposit war chest.
Margaret, 58, pension top-up before retirement
Margaret puts a £20,000 bonus into her personal pension. HMRC tops it up with basic-rate relief of £5,000 (£25,000 gross), and she reclaims another £5,000 via Self Assessment (she is a higher-rate taxpayer). Over seven years to age 65, the £25,000 gross at 4 % real becomes £32,900 inside the pension. She effectively turns £15,000 of take-home into £32,900 of future pension.
