How Compound Interest Works
Compound interest is often called the most powerful force in personal finance. Here's what it actually means, why it produces exponential growth, and how to make it work for you.
Simple interest vs compound interest
The easiest way to understand compound interest is to compare it to simple interest.
With simple interest, you earn a fixed amount of interest each year based only on your original deposit. If you save £10,000 at 5% simple interest, you earn £500 every year — no more, no less.
With compound interest, you earn interest on your growing balance — including the interest you've already earned. In year one you earn £500. In year two you earn 5% on £10,500, which is £525. In year three, 5% on £11,025 — that's £551. The amount of interest you earn grows every single year.
| Year | Simple Interest Balance | Compound Interest Balance |
|---|---|---|
| 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 |
| 40 | £30,000 | £70,400 |
£10,000 at 5% per year. Compound interest compounds annually.
By year 40, the compound balance is more than twice the simple interest balance. No extra saving required — just time.
The compound interest formula
The formula looks complex but is straightforward once broken down:
- A = ending balance (what you want to find)
- P = principal (your starting amount)
- r = annual interest rate as a decimal (e.g., 5% = 0.05)
- n = compounding frequency (times per year interest is added)
- t = time in years
If you add regular contributions, the formula extends with a future-value-of-annuity component. Our compound interest calculator handles this automatically.
How compounding frequency works
Interest can compound daily, monthly, quarterly, or annually. More frequent compounding means interest is added to your balance more often, giving each increment more time to generate its own returns.
In practice, the difference between daily and monthly compounding is small — a few pounds over many years. The difference between annual and monthly compounding is more noticeable over long periods.
The rule of 72
A useful mental shortcut: divide 72 by your interest rate to estimate how many years it takes to double your money. At 6%, 72 ÷ 6 = 12 years to double. At 8%, 72 ÷ 8 = 9 years. At 4%, 72 ÷ 4 = 18 years.
This rule is approximate but remarkably accurate for rates between 2% and 20%. It's a quick way to test whether a financial projection seems plausible.
Why starting early matters so much
The most counter-intuitive feature of compounding is how powerfully early contributions outperform later ones. Consider two savers:
- Alice saves £200/month from age 25 to 35 (10 years), then stops completely.
- Bob saves £200/month from age 35 to 65 (30 years).
At age 65, assuming 7% annual returns, Alice ends up with more money than Bob — despite only saving for 10 years versus his 30. Alice's earlier contributions had decades more time to compound. This is the most important practical insight from understanding compound interest: time is your most valuable asset.
Compound interest working against you: debt
Compound interest works the same way in reverse with debt. Credit card balances, personal loans, and mortgages also compound — meaning unpaid interest is added to your balance, generating more interest. A £5,000 credit card balance at 20% APR can grow to over £30,000 if only minimum payments are made.
This is why high-interest debt should generally be paid off before prioritising investments. You cannot reliably earn 20% from investments, but you can guarantee the equivalent by eliminating a 20% debt. See our debt payoff vs investing calculator.
How to use compound interest to build wealth
- Start as early as possible. Even small amounts invested at 25 beat large amounts invested at 40.
- Be consistent. Regular contributions compound on top of each other.
- Reinvest returns. Do not withdraw interest or dividends — let them compound.
- Use tax-efficient accounts. ISAs, Roth IRAs, and pensions shelter your compound growth from annual tax drag.
- Keep fees low. A 1% annual fund fee dramatically compounds over 30 years.
- Stay patient. Compound growth is slow to start and dramatic at the end — this is normal.
Try it yourself
Use our free compound interest calculator to model your own numbers. You can adjust the starting amount, contribution, rate, and years to see exactly how compounding affects your personal situation.