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What Is Compound Interest and How Does It Work?
Published Apr 17, 2026
What Is Compound Interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. In plain terms: your interest earns interest. Over time this creates exponential growth that is dramatically more powerful than simple interest.
Albert Einstein is often (though probably apocryphally) credited with calling compound interest "the eighth wonder of the world."
Compound vs Simple Interest
| Feature | Simple interest | Compound interest |
|---|---|---|
| Calculated on | Principal only | Principal + accumulated interest |
| Growth pattern | Linear | Exponential |
| Formula | A = P(1 + rt) | A = P(1 + r/n)^(nt) |
Example — £10,000 at 8% for 20 years:
- Simple interest: £10,000 + (10,000 × 0.08 × 20) = £26,000
- Compound interest (annual): 10,000 × (1.08)^20 = £46,610
The Compound Interest Formula
A = P × (1 + r/n)^(n × t)
Where:
- A = Final amount (principal + interest)
- P = Principal (initial deposit or loan)
- r = Annual interest rate (decimal: 8% = 0.08)
- n = Compounding periods per year
- t = Time in years
How Compounding Frequency Matters
More frequent compounding = more interest earned (slightly):
| Frequency | n | £10,000 at 8% for 10 years |
|---|---|---|
| Annual | 1 | £21,589 |
| Quarterly | 4 | £22,080 |
| Monthly | 12 | £22,196 |
| Daily | 365 | £22,255 |
The differences are relatively small for the same nominal rate. APY (Annual Percentage Yield) accounts for compounding frequency and lets you compare rates on a like-for-like basis.
The Rule of 72
A quick mental shortcut: divide 72 by the interest rate to estimate years to double your money.
Years to double = 72 ÷ annual rate %
| Rate | Years to double |
|---|---|
| 4% | 18 years |
| 6% | 12 years |
| 8% | 9 years |
| 12% | 6 years |
Compound Interest on Debt
Compound interest works against you on debt. Credit cards typically compound daily. A £5,000 balance at 25% APR, making only minimum payments, can take over 15 years to clear and cost £6,000+ in interest.
Key rule: Pay off high-interest compound debt before investing in low-return assets.
Maximising Compound Growth
- Start early. Time is the most powerful variable. £100/month from age 22 beats £200/month from age 32.
- Reinvest returns. Dividends reinvested compound; dividends withdrawn do not.
- Minimise fees. A 1% annual fund fee compounding over 30 years removes ~25% of your final balance.
- Avoid withdrawals. Every withdrawal resets the compounding base on the withdrawn amount.
Use the Interest Calculator to model compound interest growth with any rate, frequency, and time horizon.