Compound Interest — How Money Grows
Understand compound interest vs simple interest, the formula, the Rule of 72, and why starting early matters. With worked examples showing real money growth.
Albert Einstein allegedly called compound interest the "eighth wonder of the world". Whether he said it or not, compound interest is genuinely one of the most powerful forces in personal finance.
Simple vs Compound Interest
Simple interest: you earn interest only on your original amount.
Compound interest: you earn interest on your original amount plus the interest you've already earned. Interest on interest.
| Year | Simple (5%) | Compound (5%) |
|---|---|---|
| Start | £1,000 | £1,000 |
| Year 1 | £1,050 | £1,050.00 |
| Year 5 | £1,250 | £1,276.28 |
| Year 10 | £1,500 | £1,628.89 |
| Year 30 | £2,500 | £4,321.94 |
Over 30 years, compound interest gives you almost double what simple interest does.
The Formula
- A = final amount
- P = principal (starting amount)
- r = annual interest rate (as a decimal — so 5% = 0.05)
- n = times compounded per year (1 = annually, 12 = monthly)
- t = number of years
Worked Example 1 — £1,000 at 5% for 10 Years
- P = 1000, r = 0.05, n = 1, t = 10
- A = 1000 × (1 + 0.05)¹⁰
- A = 1000 × 1.05¹⁰ = 1000 × 1.6289
- A = £1,628.89
You earned £628.89 in interest — and £128.89 of that was "interest on interest".
The Power of Starting Early
Worked Example 2 — Start at 20 vs Start at 30
Both invest £200/month at 7% annual return until age 60.
- Starting at 20 (40 years): Total invested = £96,000 → Grows to ≈ £525,000
- Starting at 30 (30 years): Total invested = £72,000 → Grows to ≈ £243,000
10 extra years (£24,000 more invested) results in £282,000 more. That's the power of compound interest.
The Rule of 72
Want to know how long it takes your money to double? There's a beautifully simple shortcut:
At 6% → 72 ÷ 6 = 12 years to double. At 3% → 24 years. At 12% → 6 years.
Depreciation (Compound Decrease)
The same formula works for things losing value — just subtract the rate:
Worked Example 3 — Car Depreciation
A car worth £20,000 loses 15% of its value each year. What's it worth after 3 years?
- A = 20000 × (1 − 0.15)³
- A = 20000 × 0.85³ = 20000 × 0.6141
- A = £12,282.50
Try It Yourself
- £5,000 invested at 4% compound interest for 6 years. Final amount? (Answer: £6,326.60)
- Using the Rule of 72, how long to double at 8%? (Answer: 9 years)
- A laptop worth £1,200 depreciates by 20% per year. Value after 2 years? (Answer: £768)
Run your own compound interest calculations.
→ Open the Compound Interest Calculator