Simple vs. compound interest
Simple interest is calculated only on the original principal: I = P × r × t, where P is principal, r is the annual rate, and t is time in years.
Compound interest applies the rate to the growing balance rather than the original principal: A = P × (1 + r)^t
For £1,000 at 5% over 10 years:
| Type | Formula | Final amount |
|---|---|---|
| Simple | 1,000 × (1 + 0.05 × 10) | £1,500.00 |
| Compound (annual) | 1,000 × (1.05)^10 | £1,628.89 |
The longer the time horizon, the greater the divergence between the two.
The compound interest formula
The standard formula is:
A = P × (1 + r/n)^(n×t)
where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of compounding periods per year, and t is time in years.
For £1,000 at 6% for 5 years, compounding frequency makes a measurable difference:
| Compounding | n | Final amount |
|---|---|---|
| Annually | 1 | £1,338.23 |
| Quarterly | 4 | £1,346.86 |
| Monthly | 12 | £1,348.85 |
| Daily | 365 | £1,349.83 |
Compounding frequency: does it matter?
In principle, more frequent compounding means slightly more growth — but as the table above shows, the difference between monthly and daily is very small at typical savings rates.
The theoretical limit is continuous compounding: A = P × e^(r×t), where e is Euler's number (~2.718). For most practical purposes, monthly compounding is the most common standard in the UK and annual compounding is common in the US.
Always check the effective annual rate (EAR) rather than the nominal rate when comparing financial products — it accounts for compounding frequency and gives a true like-for-like comparison.
The Rule of 72
The Rule of 72 is a mental shortcut for estimating how long it takes to double your money. Divide 72 by the annual interest rate:
| Annual rate | Doubling time |
|---|---|
| 3% | ~24 years |
| 6% | ~12 years |
| 9% | ~8 years |
| 12% | ~6 years |
| 20% (credit card) | ~3.6 years |
The rule is accurate to within a year or two for rates between 6% and 10%. The last row shows why carrying a high-interest credit card balance is so damaging — the debt doubles in under four years if left unpaid.
Regular contributions
Lump-sum compound interest is powerful, but regular contributions amplify it further. Adding a fixed amount each month while the balance compounds creates a savings trajectory that grows exponentially over long horizons — this is the mathematical basis for pension contributions, ISAs, and index fund investing.
Our compound interest calculator supports both lump-sum and regular contribution scenarios so you can model realistic savings plans rather than theoretical single deposits.