Compound interest is often called the eighth wonder of the world, and for good reason. It’s the process that allows savings and investments to grow faster and faster over time, because you earn interest not just on the money you put in, but also on the interest you’ve already earned. Understanding how it works can help you save more effectively, invest smarter and avoid expensive debt, where compounding works against you.
This guide explains how compound interest works in plain English, with formulas, worked examples and tables. It covers simple vs compound interest, compounding frequency, AER, the Rule of 72, the impact of time, regular contributions, inflation, fees and tax, compound interest on debt and practical ways to make compounding work for you in the UK.
Table of Contents
What Is Compound Interest?
A Simple Definition
Compound interest is interest calculated on both your original amount (the principal) and any interest already added. Over time, your money earns “interest on interest,” which makes it grow at an accelerating rate.
Simple vs Compound Interest
| Feature | Simple Interest | Compound Interest |
|---|---|---|
| Interest calculated on | Original amount only | Original amount plus previous interest |
| Growth pattern | Steady, straight line | Accelerating curve |
| Long-term growth | Lower | Higher |
| Common examples | Some bonds, certain loans | Savings accounts, investments, credit cards |
Example: £10,000 at 5% a Year
| Years | Simple Interest Balance | Compound Interest Balance (Annual) |
|---|---|---|
| 1 | £10,500 | £10,500 |
| 5 | £12,500 | £12,763 |
| 10 | £15,000 | £16,289 |
| 20 | £20,000 | £26,533 |
| 30 | £25,000 | £43,219 |
After 30 years, compounding produces over £18,000 more than simple interest, without any extra money being added.
The Compound Interest Formula
The Basic Formula
A = P × (1 + r/n)^(n × t)
Where:
- A = Final amount
- P = Principal (starting amount)
- r = Annual interest rate (as a decimal, so 5% = 0.05)
- n = Number of times interest is compounded per year
- t = Number of years
Worked Example
You invest £5,000 at 4% interest, compounded annually, for 10 years:
- A = £5,000 × (1 + 0.04)^10
- A = £5,000 × 1.4802
- A = £7,401
You earn £2,401 in interest, compared with £2,000 under simple interest.
How Compounding Frequency Affects Growth
Daily, Monthly or Annual Compounding
The more often interest is added, the faster your money grows, though the difference is usually small at typical savings rates.
| Compounding Frequency | £10,000 at 5% After 1 Year |
|---|---|
| Annually | £10,500.00 |
| Quarterly | £10,509.45 |
| Monthly | £10,511.62 |
| Daily | £10,512.67 |
Understanding AER
UK savings accounts show an AER (Annual Equivalent Rate). It tells you what interest you’d earn over a year if interest were compounded and left in the account. AER makes it easier to compare accounts with different compounding frequencies.
Gross Rate vs AER
- Gross rate: The interest rate before tax, without compounding
- AER: The rate including the effect of compounding
When comparing savings accounts, always compare AERs.
The Rule of 72: A Handy Shortcut
How Long Will It Take to Double Your Money?
Divide 72 by your annual interest rate (or return) to estimate how many years it takes to double your money.
Years to double ≈ 72 ÷ Interest rate
| Annual Return | Approximate Years to Double |
|---|---|
| 2% | 36 years |
| 3% | 24 years |
| 4% | 18 years |
| 5% | 14.4 years |
| 6% | 12 years |
| 8% | 9 years |
| 10% | 7.2 years |
The Rule of 72 also works in reverse for debt and inflation. At 3.5% inflation, prices roughly double in about 20 years.
Why Time Is Your Biggest Advantage
Starting Early Makes a Huge Difference
The longer your money compounds, the more powerful the effect. Small amounts invested early can outgrow larger amounts invested later.
Example: Starting at 25 vs 35
Both people invest £200 a month at a 6% annual return (compounded monthly) until age 65.
| Investor | Starts At | Years Investing | Total Contributed | Approximate Value at 65 |
|---|---|---|---|---|
| Alex | 25 | 40 | £96,000 | £398,000 |
| Sam | 35 | 30 | £72,000 | £201,000 |
Alex contributes only £24,000 more but ends up with nearly twice as much, simply by starting ten years earlier.
Illustrative only. Investment returns aren’t guaranteed and can fall as well as rise.
The Snowball Effect
In the early years, most growth comes from your contributions. Over time, compounding takes over and the returns themselves become the main driver of growth.
The Power of Regular Contributions
Adding Money Regularly
Compound interest becomes even more powerful when you add money regularly, such as monthly savings or pension contributions.
Example: £200 a Month at 6% a Year
| Years | Total Contributed | Approximate Value | Growth From Returns |
|---|---|---|---|
| 5 | £12,000 | £13,950 | £1,950 |
| 10 | £24,000 | £32,800 | £8,800 |
| 20 | £48,000 | £92,400 | £44,400 |
| 30 | £72,000 | £200,900 | £128,900 |
After 30 years, investment growth makes up well over half of the final value.
Increase Contributions Over Time
Raising your monthly contributions as your income grows, even by small amounts, can dramatically boost long-term results.
Compound Interest vs Compound Returns
Savings vs Investments
- Savings accounts earn compound interest at a set or variable rate
- Investments (such as shares and funds) earn compound returns through price growth and reinvested dividends
Investment returns aren’t guaranteed and can be negative in some years, but historically, shares have offered higher long-term returns than cash, with more risk.
Reinvesting Dividends
Reinvesting dividends allows them to buy more shares or fund units, which then earn their own dividends. Accumulation funds do this automatically.
| Type | How It Grows | Risk |
|---|---|---|
| Easy-access savings | Compound interest | Very low |
| Fixed-rate savings | Compound interest (often paid at maturity) | Very low |
| Stocks and shares (with dividends reinvested) | Compound returns | Medium to high |
| Bonds (with income reinvested) | Compound returns | Low to medium |
| Pensions | Compound returns plus tax relief | Varies by investment |
Inflation: The Hidden Enemy of Compounding
Real vs Nominal Returns
Inflation reduces the purchasing power of your money. Your real return is roughly your interest rate minus inflation.
Real return ≈ Interest rate − Inflation rate
Current UK Context
Interest rates and inflation have risen again in late 2026. At its November 2026 meeting, the Bank of England’s Monetary Policy Committee (MPC) voted by a majority of 8–1 to increase Bank Rate by 0.25 percentage points, to 4%. The Bank noted that UK CPI inflation increased to 3.5% in September.
Example
| Savings Rate | Inflation Rate | Approximate Real Return |
|---|---|---|
| 4.5% | 3.5% | +1.0% |
| 3.5% | 3.5% | 0% |
| 2.0% | 3.5% | −1.5% |
If your savings earn less than inflation, your money is losing value in real terms, even though the balance is rising.
How Fees Reduce Compound Growth
Small Fees, Big Impact
Fees compound too, reducing your returns year after year.
Example: £10,000 Invested for 30 Years
| Annual Return After Fees | Approximate Final Value |
|---|---|
| 6.0% (no fees) | £57,435 |
| 5.5% (0.5% fees) | £49,840 |
| 5.0% (1% fees) | £43,219 |
| 4.5% (1.5% fees) | £37,453 |
A 1% annual fee could cost over £14,000 on a £10,000 investment over 30 years. Choosing low-cost funds and platforms helps keep more of your returns compounding for you.
How Tax Affects Compound Interest
Tax Reduces What Compounds
If tax is taken from your interest or returns each year, less money remains to compound.
UK Savings Tax Allowances
| Allowance | Amount |
|---|---|
| Personal Savings Allowance (basic-rate taxpayers) | £1,000 |
| Personal Savings Allowance (higher-rate taxpayers) | £500 |
| Personal Savings Allowance (additional-rate taxpayers) | £0 |
| Starting rate for savings | Up to £5,000 (if other income is low) |
| Dividend Allowance | £500 |
| ISA allowance | £20,000 a year |
Changes Coming in April 2027
Savers should prepare for higher tax rates and a lower cash ISA limit. From 6 April 2027, savings income tax rates will increase by two percentage points across all bands to 22% (basic rate), 42% (higher rate) and 47% (additional rate). In addition, from 6 April 2027 the annual ISA cash limit will be set at £12,000, within the overall annual ISA limit of £20,000, with over-65s keeping the full £20,000 cash limit.
Use Tax Wrappers
Holding savings and investments in ISAs and pensions lets your money compound without income tax or capital gains tax being taken out, which becomes even more valuable as tax rates rise.
Compound Interest on Debt: When It Works Against You
Debt Grows Too
Compound interest isn’t always your friend. Credit cards, overdrafts, payday loans and some personal loans charge interest on unpaid balances, and that interest can compound.
Example: Credit Card Debt
A £3,000 credit card balance at 24% APR (charged monthly at about 2%), with no payments made:
| Time | Approximate Balance |
|---|---|
| Start | £3,000 |
| 6 months | £3,378 |
| 1 year | £3,805 |
| 2 years | £4,826 |
| 3 years | £6,120 |
Illustrative only. Actual charges depend on the card terms.
Minimum Payments Keep You Paying
Paying only the minimum on a credit card can mean it takes many years to clear the balance, with far more paid in interest than the original debt.
Tackle High-Interest Debt First
Paying off a credit card charging 24% is effectively a guaranteed 24% return, far more than most savings accounts or investments can offer.
How to Make Compound Interest Work for You
1. Start as Early as Possible
Even small amounts benefit from long periods of compounding.
2. Save and Invest Regularly
Set up automatic monthly transfers to savings, ISAs or pensions.
3. Reinvest Interest and Dividends
Leave interest in the account and choose accumulation funds where appropriate.
4. Choose Good Rates
Compare savings accounts by AER and switch when better rates are available.
5. Keep Costs Low
Choose low-cost index funds and compare platform fees.
6. Use ISAs and Pensions
Shield your growth from tax.
7. Beat Inflation
For long-term goals, consider investing in diversified funds rather than holding all your money in cash.
8. Avoid Withdrawing Early
Every withdrawal interrupts compounding.
9. Pay Off High-Interest Debt
Stop compound interest working against you.
10. Use Your Workplace Pension
Employer contributions and tax relief give your money a head start before compounding even begins.
Compound Interest Calculators
Plan Your Goals
Online compound interest calculators let you test different scenarios:
- Starting balance
- Monthly contributions
- Interest rate or expected return
- Compounding frequency
- Time period
- Inflation
Use them to see how small changes, such as starting earlier or contributing a little more, affect your final result.
Common Compound Interest Mistakes
Waiting to Start
Delaying even a few years can significantly reduce long-term growth.
Ignoring Inflation
Growth that doesn’t beat inflation loses purchasing power.
Overlooking Fees
High fees quietly eat away at compound returns.
Leaving Money in Low-Interest Accounts
Old or “loyalty” accounts often pay far less than the best rates.
Carrying High-Interest Debt
Compound interest on debt can wipe out any savings gains.
Withdrawing Too Often
Frequent withdrawals reset the snowball.
Expecting Guaranteed Investment Returns
Investment returns vary year to year and can be negative, especially in the short term.
Final Thoughts
Compound interest is one of the most powerful forces in personal finance. By earning returns on both your original money and the interest or returns it has already earned, your savings and investments can grow at an accelerating rate over time. The biggest factors are time, regular contributions, the rate of return, fees, tax and inflation.
Start early, save regularly, reinvest your returns, keep costs low and use ISAs and pensions to protect your growth from tax, especially with savings income tax rising and the cash ISA limit falling to £12,000 for under-65s from April 2027. At the same time, avoid high-interest debt, where compounding works against you. With patience and consistency, compound interest can turn modest savings into significant long-term wealth.
Frequently Asked Questions
1. What is the difference between simple and compound interest?
Simple interest is calculated only on your original amount, while compound interest is calculated on both the original amount and previously earned interest.
2. How often is interest compounded on UK savings accounts?
It varies by account, from daily to monthly or annually, which is why comparing the AER is the best way to compare savings accounts.
3. What is the Rule of 72?
The Rule of 72 estimates how long it takes to double your money by dividing 72 by your annual interest rate or return.
