Compound interest is often called the eighth wonder of the world — and for good reason. It’s the mechanism that can turn small, regular savings into life-changing wealth over time. It’s also the mechanism that can quietly crush you under a mountain of debt if you’re on the wrong side of it.
This guide explains exactly how it works, shows you the maths behind it, and gives you the tools to use it to your advantage.
What is compound interest?
At its simplest: compound interest is interest earned on interest.
With simple interest, you only ever earn interest on your original deposit. With compound interest, each period’s interest is added to your balance, and the next period you earn interest on the larger number. The result is exponential growth rather than linear growth.
Consider a £1,000 deposit at 10% per year:
| Year | Simple interest balance | Compound interest balance |
|---|---|---|
| 1 | £1,100 | £1,100 |
| 5 | £1,500 | £1,611 |
| 10 | £2,000 | £2,594 |
| 20 | £3,000 | £6,727 |
| 30 | £4,000 | £17,449 |
The gap between the two columns — that’s compound interest at work.
The compound interest formula
The standard formula is:
A = P(1 + r/n)^(nt)
Where:
- A = final amount
- P = principal (starting balance)
- r = annual interest rate (as a decimal, so 7% = 0.07)
- n = number of times interest compounds per year
- t = number of years
A worked example
You invest £5,000 at 7% per year, compounded monthly, for 10 years:
- P = £5,000
- r = 0.07
- n = 12
- t = 10
A = 5000 × (1 + 0.07/12)^(12×10) = 5000 × (1.00583)^120 ≈ £10,009
Your money has effectively doubled in 10 years — purely through compounding. No additional deposits needed.
How compounding frequency affects growth
The more frequently interest compounds, the more you earn. The difference between annual and daily compounding is more significant at higher interest rates:
| Compounding frequency | £10,000 at 8% after 20 years |
|---|---|
| Annually | £46,610 |
| Quarterly | £48,010 |
| Monthly | £49,268 |
| Daily | £49,530 |
Daily beats annual by nearly £3,000 on the same principal over 20 years.
The Rule of 72
There’s a beautifully simple mental shortcut called the Rule of 72: divide 72 by your annual 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 to double
- At 12%: 72 ÷ 12 = 6 years to double
This is an approximation, but it’s accurate enough for quick mental maths.
Regular contributions turbocharge the effect
A one-time deposit grows impressively. A regular monthly contribution combined with compound interest can produce extraordinary results.
Example: £1,000 starting balance + £200/month at 7% for 20 years:
- Total you put in: £49,000
- Final balance: approximately £108,000
- Interest earned: £59,000 — more than you contributed yourself
That extra £59,000 is purely the compound interest on your contributions and the interest already earned.
Try this exact scenario with our free compound interest calculator →
The dark side: compound interest on debt
Everything above applies equally to debt — just in the opposite direction. Credit card balances, high-interest loans, and payday loans all use compound interest against you.
A £2,000 credit card balance at 20% APR, if you only pay the minimum each month, can take over 10 years to pay off and cost you more in interest than your original balance.
The lesson: compound interest is your best friend in savings and your worst enemy in debt. Eliminate high-interest debt aggressively before investing.
How to make compound interest work for you
- Start early. Time is the most powerful variable in the formula. Starting at 25 vs 35 can mean double the final balance at retirement.
- Never break the compound chain. Withdrawing principal resets the clock. Let the interest compound.
- Reinvest returns. Dividends reinvested (DRIP) are compound interest on steroids.
- Choose high-yield accounts. A 4% savings account vs a 0.5% account makes a huge difference over 20 years.
- Add regularly. Even small monthly additions massively amplify the final outcome.
Use our free calculator
Want to see exactly how much a specific scenario will grow? Our compound interest calculator lets you:
- Set any starting balance and monthly contribution
- Choose your interest rate and compounding frequency
- Switch between currencies
- See a year-by-year growth chart and table
No sign-up, no ads, just answers.