Albert Einstein is often credited with calling compound interest "the eighth wonder of the world — he who understands it, earns it; he who doesn't, pays it." Whether he actually said it is debated, but the sentiment is spot-on. Compound interest is one of the most powerful forces in personal finance, and understanding it can be the difference between building real wealth and paying off debt forever.
This guide explains exactly how compound interest works, shows you the formula step-by-step, and walks through real examples so you can see the numbers yourself.
Simple interest earns a return only on your original principal. Compound interest earns a return on your principal plus all previously earned interest. That distinction seems small at first, but over time it creates an enormous gap.
Think of it like a snowball rolling downhill. The larger the snowball gets, the more snow it picks up per revolution. Your investment works the same way — the more you accumulate, the faster it grows.
Breaking down each variable:
The same £5,000 at 7% over 20 years, but with different compounding frequencies:
| Compounding | n | Final Value | Interest Earned |
|---|---|---|---|
| Annually | 1 | £19,348 | £14,348 |
| Quarterly | 4 | £20,097 | £15,097 |
| Monthly | 12 | £20,193 | £15,193 |
| Daily | 365 | £20,242 | £15,242 |
Daily compounding beats annual compounding by nearly £900 on just £5,000 — and that gap widens dramatically at larger amounts or longer time periods.
Want a quick mental estimate of how long it takes to double your money? Divide 72 by your annual interest rate.
The Rule of 72 works in both directions. It also tells you how quickly debt grows if you don't pay it down — a credit card charging 24% interest doubles what you owe in just 3 years.
| Year | Simple Interest (7%) | Compound Interest (7%) |
|---|---|---|
| 1 | £5,350 | £5,362 |
| 5 | £6,750 | £7,036 |
| 10 | £8,500 | £9,900 |
| 20 | £12,000 | £19,348 |
| 30 | £15,500 | £38,061 |
At 30 years, compound interest produces more than twice the return of simple interest on the same initial investment. This is why starting early matters so much.
"The best time to plant a tree was 20 years ago. The second best time is now."
Consider two investors, both earning 8% per year compounded annually:
At age 65, Alex ends up with approximately £472,000 — Sam ends up with approximately £367,000. Alex invested a third of the money but started 10 years earlier. Time in the market beats timing the market.
The same mathematics that grows your savings also grows your debt. Credit cards, payday loans, and buy-now-pay-later schemes all use compound interest — sometimes daily. A £2,000 credit card balance at 22% APR compounded monthly grows to over £5,300 in 5 years if you make no payments.
This is why high-interest debt should always be the first financial priority — the compound effect is working in reverse on every outstanding balance.
Enter your principal, interest rate, compounding frequency, and time period to see exactly how your money grows — with a year-by-year breakdown.
Open Calculator →A "good" rate depends on the context. For a savings account in 2026, 4–5% is strong. For long-term stock market investments, historical averages suggest 7–10% annually (before inflation). For debt, any rate is bad — prioritise eliminating it.
Not exactly in the same formula, but the principle applies. When dividends are reinvested and share prices appreciate, the overall return compounds. Index funds that reinvest dividends are one of the most common ways to benefit from compounding.
In Excel or Google Sheets, use: =P*(1+r/n)^(n*t) where you replace each variable with its cell reference. Or use the FV function: =FV(r/n, n*t, 0, -P).
APY (Annual Percentage Yield) accounts for compounding and gives you the true annual return. APR (Annual Percentage Rate) does not account for compounding within the year. Always compare savings accounts using APY, not APR.