The compound interest formula
Where: A = final amount, P = principal (starting amount), r = annual interest rate (as decimal), n = number of times compounded per year, t = time in years.
Example: £10,000 at 7% annual interest, compounded monthly, for 20 years:
A = 10,000 × (1 + 0.07/12)^(12×20) = 10,000 × (1.005833)^240 = 10,000 × 4.0387 = £40,387
That £10,000 grew to over £40,000 — more than quadrupling — without any additional contributions. This is the power of compound interest.
How compounding frequency affects your returns
On the same £10,000 at 7% over 20 years, different compounding frequencies produce:
- Annually: £38,697
- Monthly: £40,388
- Daily: £40,535
- Continuously: £40,552
Daily compounding produces only £164 more than annual compounding over 20 years on this amount. The difference is real but modest — compounding frequency matters far less than rate and time.
The Rule of 72 — the quick mental shortcut
Divide 72 by the interest rate to find roughly how many years it takes to double your money:
- 4% return: 72 ÷ 4 = 18 years to double
- 7% return: 72 ÷ 7 ≈ 10 years to double
- 10% return: 72 ÷ 10 = 7.2 years to double
- 12% return: 72 ÷ 12 = 6 years to double
Adding regular contributions: the real wealth-building formula
The greatest accelerant to compound growth is regular contributions. On top of the lump sum formula, regular monthly contributions of £200 at 7% for 20 years adds approximately £104,400 in final value — far more than the initial £10,000 lump sum.
The total final value with £10,000 initial + £200/month at 7% over 20 years = approximately £145,000. The total invested = £10,000 + (£200 × 240 months) = £58,000. The remaining £87,000 is pure compound interest.
Compound interest in different account types
High-yield savings accounts (US): Compound daily, APY 4.5–5.5% in 2025. FDIC insured to $250,000.
ISAs (UK): Cash ISAs pay up to 5% and compound annually or monthly. Stocks & Shares ISAs compound through growth and dividends, historically averaging 7–8% annually over long periods.
Superannuation (Australia): Compounding occurs through investment returns within your super fund, averaged 8–9% annually over the past decade across balanced options.
Index funds: The S&P 500 has returned approximately 10% annually (nominal) over its history. At 10%, money doubles every 7.2 years, quadruples every 14.4 years.
The enemy of compound interest: inflation and fees
At 3% annual inflation, the real purchasing power of your returns is reduced significantly. A 7% nominal return with 3% inflation yields a real return of approximately 4% (the Fisher equation: real rate ≈ nominal rate − inflation rate).
Investment fees work against you through the same compounding mechanism. A 1% annual management fee on £100,000 over 30 years at 7% growth costs approximately £78,000 in forgone compound growth. This is why index funds with expense ratios under 0.1% dramatically outperform equivalent actively managed funds with 1–2% fees over long periods.