How compound interest works

Albert Einstein supposedly called compound interest the eighth wonder of the world. Whatever the origin, the maths is genuinely remarkable: given time, compounding turns modest savings into serious money. Here’s how it works, with real numbers.

The basic idea

With simple interest, you earn a fixed percentage of your original deposit each year. With compound interest, you earn interest on your interest — your base grows every year, so the amount of interest grows too.

Worked example — £10,000 at 5%.

• Year 1: £10,000 + £500 interest = £10,500
• Year 2: £10,500 + £525 = £11,025
• Year 5: £12,763
• Year 10: £16,289
• Year 20: £26,533

The growth isn’t steady — it accelerates, because each year’s interest is earned on a larger balance.

Time is the magic ingredient

The single biggest factor in compounding is time, not the amount you save.

Two savers. Amy saves £200 a month from age 25 to 35 (£24,000 total), then stops. Ben saves £200 a month from age 35 to 65 (£72,000 total) — three times as much. At 6% annual growth, Amy’s money is worth more by age 65, because hers had an extra ten years to compound.

That’s the argument for starting today, even with a small amount.

The rule of 72

A quick mental tool: divide 72 by the interest rate to estimate doubling time.

• 3% → ~24 years to double
• 5% → ~14.4 years
• 6% → ~12 years
• 8% → ~9 years

Where compounding lives

• Savings accounts — compound interest on your balance (daily or monthly)
• ISAs — the same, tax-free
• Pensions — decades of compounding, boosted by tax relief and employer contributions
• Debt — the same maths in reverse, which is why clearing high-interest balances is an “investment” you can’t beat

The rule of thumb

Stay invested, don’t touch it, and let the rate × time do the work. As a benchmark, savings accounts in 2026 are paying around 4–5% and long-term markets roughly 5–7% above inflation — but always compare current rates on comparison sites.

Run your own numbers

The savings calculator models monthly contributions and compounding frequency over any number of years — try starting balances, £100 vs £300 a month, and see what a decade of patience looks like.