Albert Einstein reportedly called compound interest the "eighth wonder of the world." Whether or not he actually said it, the mathematics behind it is genuinely extraordinary. Compound interest turns modest regular savings into significant wealth over time — but only if you understand how it works and start early enough. This guide explains everything UK savers and investors need to know.
Simple Interest vs Compound Interest — The Key Difference
Simple interest is calculated only on your original deposit (the principal). If you deposit £10,000 at 5% simple interest for 10 years, you earn £500/year = £5,000 total. Your pot grows to £15,000.
Compound interest is calculated on your principal plus all the interest you have already earned. That same £10,000 at 5% compounded annually for 10 years grows to £16,289 — an extra £1,289 just from compounding. Over 30 years, the difference is enormous: simple interest gives £25,000; compound interest gives £43,219.
The Compound Interest Formula
The formula is: A = P × (1 + r/n)^(n×t)
- A = Final amount
- P = Principal (initial deposit)
- r = Annual interest rate (as a decimal — 5% = 0.05)
- n = Compounding frequency per year (1 = annual, 12 = monthly, 365 = daily)
- t = Time in years
You do not need to do this manually — use our Compound Interest Calculator to see the results instantly.
How Compounding Frequency Affects Growth
The same interest rate compounded more frequently produces slightly higher returns. Using £10,000 at 5% for 10 years:
- Annual compounding: £16,289
- Monthly compounding: £16,470
- Daily compounding: £16,487
The difference is modest at lower rates and shorter periods, but the principle matters when comparing savings accounts. The AER (Annual Equivalent Rate) in the UK standardises all savings accounts to an annual equivalent — so you can always compare AERs directly, regardless of how frequently each account compounds.
What Is AER?
AER stands for Annual Equivalent Rate. It is the rate that shows what you would earn in a year if interest was compounded and left in the account for the full year. UK law requires savings providers to display AER so consumers can make fair comparisons. Always use AER — not gross rate or monthly rate — when comparing savings accounts.
The Rule of 72 — How Long to Double Your Money
Divide 72 by your annual interest rate to get an estimate of how many years it takes to double your money at compound interest:
- At 2%: doubles in 36 years
- At 4%: doubles in 18 years
- At 6%: doubles in 12 years
- At 8%: doubles in 9 years
- At 10%: doubles in 7.2 years
This is why the difference between a 3% and a 6% return on a Stocks & Shares ISA is not just double — it is the difference between doubling every 24 years versus every 12 years.
Why Starting Early Matters So Much
Consider two people:
- Alice saves £200/month from age 22 to 32 (10 years), then stops. Total contributions: £24,000.
- Bob waits until age 32, then saves £200/month until age 62 (30 years). Total contributions: £72,000.
At a 7% annual return, by age 62: Alice has approximately £270,000. Bob has approximately £243,000 — despite saving three times as much money. Alice's 10-year head start with compound growth beats Bob's 30 years of contributions.
Compound Interest in Practice — UK Savings Options
- Cash ISA: Tax-free interest compounded monthly or annually. Current rates 3.5–5%. Great for medium-term savings with zero tax drag.
- Savings account: Similar rates but interest above your Personal Savings Allowance (£1,000 basic rate, £500 higher rate) is taxable, which reduces effective compounding.
- Stocks & Shares ISA: Compounding via reinvested dividends and capital growth. Historically 7–10%/year over the long term. Capital at risk, but tax-free growth on potentially much higher returns.
- Pension: Compounding plus upfront tax relief. Your contributions get boosted 20–40%+ before they even start growing. The combined effect is the most powerful legal wealth-building tool available to UK residents.
The Impact of Inflation on Compound Returns
Compound interest figures are usually quoted in nominal terms — they do not account for inflation. To find your real return, subtract the inflation rate from your nominal rate. If you earn 4% but inflation is 3%, your real return is approximately 1%. This means your purchasing power grows by 1% per year, not 4%. For savings to genuinely build wealth, your rate should outpace inflation — which is why long-term equity investing via Stocks & Shares ISAs tends to beat cash savings over 10+ year periods.