Compound Interest Explained: How Your Money Grows Over Time
Understand compound interest with real examples, frequency comparison (daily vs monthly vs annual), and why starting early matters.
What Is Compound Interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. In simple terms: you earn interest on your interest. This creates exponential growth over time — the longer money compounds, the faster it accelerates. Albert Einstein is often (probably apocryphally) credited with calling it the "eighth wonder of the world." Whether or not he said it, the mathematics backs up the sentiment.
Compound Interest vs Simple Interest
Simple interest is calculated only on the original principal. If you invest £5,000 at 5% simple interest for 10 years, you earn £250 per year = £2,500 total interest, leaving you with £7,500.
Compound interest earns interest on the growing balance. That same £5,000 at 5% compounded annually for 10 years grows to £8,144 — £644 more than simple interest, purely from compounding. Over 30 years the gap becomes enormous.
The Compound Interest Formula
The standard formula is: A = P(1 + r/n)^(nt)
- A = final amount
- P = principal (initial investment)
- r = annual interest rate (as a decimal, e.g. 5% = 0.05)
- n = number of times interest compounds per year
- t = time in years
Worked Example: £5,000 at 5% Over 10 Years
| Compounding Frequency | Final Balance | Total Interest |
|---|---|---|
| Simple interest | £7,500 | £2,500 |
| Annually | £8,144 | £3,144 |
| Monthly | £8,193 | £3,193 |
| Daily | £8,202 | £3,202 |
More frequent compounding does help, but the difference between monthly and daily is small. The rate and the time invested matter far more than compounding frequency.
The Rule of 72
The Rule of 72 is a quick mental shortcut: divide 72 by your annual interest rate to estimate how many years it takes to double your money. At 5%, money doubles in roughly 72 ÷ 5 = 14.4 years. At 8%, it doubles in 9 years. At 10%, just 7.2 years.
This also works in reverse to understand inflation. At 3% inflation, the purchasing power of your savings halves in 24 years — which is why keeping large sums in low-rate cash accounts over the long term erodes real wealth.
Why Starting Early Makes a Massive Difference
The most powerful variable in compound interest is time. Consider three investors who each invest £200 per month into a global index fund averaging 7% per year:
| Start Age | Stop Investing | Total Invested | Balance at 65 |
|---|---|---|---|
| 25 | 65 (40 years) | £96,000 | £524,000 |
| 35 | 65 (30 years) | £72,000 | £243,000 |
| 45 | 65 (20 years) | £48,000 | £104,000 |
Starting at 25 rather than 35 produces more than double the final balance despite investing only £24,000 more. The extra decade of compounding does more work than the money itself.
ISA vs Cash Savings Account for Compound Growth
If your savings earn interest taxable at 20% or 40%, you are compounding on an after-tax return. A higher-rate taxpayer earning 5% in a taxable account only keeps 3% net. Inside a Cash ISA or Stocks and Shares ISA, 100% of the return compounds tax-free — the difference over 20–30 years is substantial. The ISA annual allowance is £20,000, and unused allowance cannot be carried forward, so prioritising it each tax year (before 5 April) captures the maximum benefit.
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