Simple Interest vs Compound Interest
**Simple interest** pays interest only on the original principal. £1,000 at 5% per year earns £50 every year, forever.
- Year 1: £1,000 × 5% = £50 interest → £1,050
- Year 2: £1,050 × 5% = £52.50 interest → £1,102.50
- Year 3: £1,102.50 × 5% = £55.13 interest → £1,157.63
The extra £2.50 in year 2 came from the year 1 interest earning interest. That's compounding.
The Formula
A = P × (1 + r/n)^(nt)
A= final amountP= principal (initial investment)r= annual interest rate as a decimal (5% = 0.05)n= compounding frequency (times 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) = £40,387
That's £30,387 of gains on a £10,000 investment — more than tripling your money without adding a penny.
Why Compounding Frequency Matters
The more frequently interest compounds, the more you earn — but the difference is smaller than most people expect:
- Annual compounding: £38,697
- Monthly compounding: £40,387
- Daily compounding: £40,540
- Continuous compounding: £40,552
Monthly vs daily makes less than £200 difference over 20 years. The rate and time period matter far more than compounding frequency.
The Rule of 72
A quick mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money.
- 6% return → 72 ÷ 6 = 12 years to double
- 8% return → 72 ÷ 8 = 9 years to double
- 12% return → 72 ÷ 12 = 6 years to double
This works because of how exponential growth behaves. It's an approximation but accurate to within 1% for rates between 6% and 10%.
The Real Power: Time in the Market
- After 10 years: £2,159
- After 20 years: £4,661
- After 30 years: £10,063
- After 40 years: £21,725
The final 10-year period adds more (£11,662) than the first 30 years combined (£9,063). This is why starting early matters so much more than the exact rate you achieve.
Compound Interest Working Against You
Compound interest is equally powerful on debt. Credit cards typically charge 20–30% APR. A £3,000 balance at 25% with minimum payments (1% of balance per month) takes over 15 years to pay off and costs more than £3,000 in interest alone.
The same mechanics that build wealth in investments destroy it on high-interest debt. Paying down 25% APR debt is a guaranteed 25% return — better than almost any investment.
Inflation: The Negative Compounder
Inflation compounds too, in the opposite direction. At 3% annual inflation, £1,000 today is worth only £744 in 10 years in real terms. Any investment return below inflation represents a real loss of purchasing power, even if the nominal number is positive.
For long-term wealth building, the target is real returns (nominal return minus inflation) that are meaningfully positive.
NoxaKit's Compound Interest Calculator handles all of these scenarios — lump sum investments, regular contributions, varying compounding frequencies, and inflation adjustment.