Compound interest is interest calculated on both the initial principal and the accumulated interest from prior periods. Albert Einstein allegedly called it "the eighth wonder of the world" - the longer the time horizon, the more dramatic the effect.
The compound interest formula
A = P(1 + r)^n
Where:
- A = final amount
- P = principal (initial investment)
- r = interest rate per period
- n = number of periods
Example: £10,000 invested at 6% for 20 years
A = £10 000 × (1.06)^20 = £10 000 × 3.207 = £32 071
The £10,000 grew by £22,071 - the power of compounding.
With regular contributions (savings formula)
A = P(1+r)^n + C × ((1+r)^n - 1) / r
Where C = regular contribution per period.
Example: £500/month for 30 years at 5% → final value ≈ £416,000 (from only £180,000 contributed).
The Rule of 72
Quickly estimate how long it takes to double your money:
Years to double ≈ 72 / annual rate (%)
| Rate | Doubling time |
|---|---|
| 3% | 24 years |
| 5% | 14.4 years |
| 7% | 10.3 years |
| 10% | 7.2 years |
Compounding frequency matters
At 5% nominal rate, different compounding frequencies produce:
| Frequency | Effective annual rate |
|---|---|
| Annual | 5.000% |
| Quarterly | 5.095% |
| Monthly | 5.116% |
| Daily | 5.127% |