Guides 7 min read
Compound Interest — How Your Money Grows (or Costs) Exponentially
Albert Einstein allegedly called compound interest the eighth wonder of the world. Whether or not he said it, the maths is indisputable: money earning interest on its own interest grows exponentially. Understanding this single concept changes how you think about saving, investing and borrowing.
Simple vs compound interest
Simple interest pays a fixed amount on the original principal each period. If you invest £10,000 at 5% simple interest, you earn £500 every year regardless of how long the investment runs. After 20 years: £10,000 + (20 × £500) = £20,000.
Compound interest pays interest on the principal plus all previously accumulated interest. The same £10,000 at 5% compounded annually becomes £26,533 after 20 years — 33% more than simple interest. The longer the time horizon, the wider the gap.
The compound interest formula
The core formula is: A = P(1 + r/n)nt
- A = final amount
- P = principal (starting amount)
- r = annual interest rate (decimal)
- n = compounds per year
- t = time in years
When you add regular contributions (PMT), the formula extends: A = P(1+r/n)nt + PMT × [((1+r/n)nt − 1) / (r/n)]. This is what the compound interest calculator uses.
How compounding frequency matters
More frequent compounding (monthly vs annually) produces a slightly higher effective rate. £10,000 at 5% for 10 years:
- Annually: £16,289
- Quarterly: £16,436
- Monthly: £16,470
- Daily: £16,487
The difference between annual and monthly is modest (~1.1% over 10 years). Between monthly and daily it is negligible. In practice, most savings accounts compound daily and credit interest monthly.
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. At 6% → 72/6 = 12 years. At 8% → 9 years. At 4% → 18 years.
The rule works in reverse for debt: a credit card at 24% APR doubles your balance in just 3 years if unpaid. This makes compound interest your best friend for saving and your worst enemy for borrowing.
The impact of starting early
Consider two savers:
- Saver A invests £200/month from age 22 to 32 (10 years, £24,000 total), then stops.
- Saver B invests £200/month from age 32 to 62 (30 years, £72,000 total).
At 7% annual return: Saver A has ~£400,000 at age 62. Saver B has ~£227,000. Despite investing three times less money, Saver A wins because those early contributions had 40 years to compound. This is why pension auto-enrolment starts early.
Inflation: the silent compounder working against you
Inflation also compounds. At 3% annual inflation, prices double every 24 years. A basket of goods costing £100 today costs £181 in 20 years. This means your investments need to earn above inflation (the "real return") to actually grow your purchasing power.
The compound interest calculator has an inflation toggle — enable it to see your future balance expressed in today's money. A nominal £50,000 at 2.5% inflation is worth only about £38,000 in real terms over 10 years.
Practical applications
Use compound interest in your favour:
- Savings: Start early, contribute regularly, reinvest all interest.
- Debt: Pay above minimum to stop interest compounding against you. The credit card payoff calculator shows the true cost of minimum payments.
- Retirement: The earlier you start, the less you need to contribute. A 25-year-old saving £300/month reaches retirement with more than a 35-year-old saving £600/month.
Frequently asked questions
What return rate should I assume for planning?
For cash savings: use your actual account rate (currently 4–5% in the UK). For diversified equity investments: 5–7% real (after inflation) is the long-term historical average. Be conservative — using 5% real gives a margin of safety.
Does compound interest apply to ISAs?
Yes. Interest, dividends and capital gains within an ISA compound tax-free. This makes ISAs more powerful over long time horizons than taxable accounts.
How does compound interest work on debt?
The same way but against you. Unpaid credit card balances compound monthly at the card's APR. A £5,000 balance at 22% APR accrues over £90 in interest in the first month alone, and that interest compounds if unpaid.
Is "continuous compounding" better than daily?
Mathematically yes (using e^rt), but the practical difference from daily compounding is fractions of a penny. No retail product offers continuous compounding.