How Does Compound Interest Work?

What is Compound Interest?

Compound interest is interest calculated on both your initial principal and the interest you have already earned. Each period, your interest is added to your balance, and the next period's interest is calculated on that larger balance. The result is exponential growth — money making money on top of money.

The contrast with simple interest makes the difference clear. With simple interest, you earn the same amount each period — £500 per year on a £10,000 deposit at 5%. With compound interest, you earn £500 in year one, £525 in year two, £551 in year three and so on. The amounts accelerate over time because each year's interest becomes part of the base for next year's calculation.

According to data from major global investment firms, the average global stock market has returned approximately 7-10% annually over long periods before accounting for inflation. At 8% compound annual growth, £10,000 becomes £46,610 after 20 years and £217,245 after 40 years — entirely through compounding, without adding another penny.

The Compound Interest Formula

The standard compound interest formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of compounding periods per year and t is the number of years.

For a practical example: £10,000 at 5% compounded annually over 10 years: A = 10,000 × (1.05)^10 = £16,289. The interest earned is £6,289 on a £10,000 principal — a 62.89% return over 10 years. The same amount with simple interest at 5% for 10 years would yield only £15,000 — £1,289 less. The gap widens dramatically over longer periods.

Compounding Frequency

More frequent compounding produces slightly higher returns. Using £10,000 at 5% for 10 years: annually yields £16,289, quarterly £16,436, monthly £16,470 and daily £16,487. The difference between annual and daily compounding is £198 over 10 years at 5% — small at typical savings rates but more significant at higher rates or over longer periods.

In the UK, savings accounts quote AER (Annual Equivalent Rate) which already accounts for compounding frequency. In the US, APY (Annual Percentage Yield) serves the same purpose. These standardised rates make it easy to compare accounts fairly regardless of how frequently they compound.

The Rule of 72

The Rule of 72 is one of the most useful mental shortcuts in personal finance. Divide 72 by the annual interest rate to estimate how long it takes for money to double. At 6% annual return, money doubles in approximately 12 years (72 ÷ 6 = 12). At 8%, it doubles in 9 years. At 4%, it takes 18 years.

The rule works in reverse too. To find what rate is needed to double money in a given time, divide 72 by the number of years. To double money in 10 years requires approximately 7.2% annual return. This is why global equity index funds, which have historically returned 7-10% annually, are widely considered effective long-term wealth-building vehicles — they are broadly consistent with doubling money roughly every 7-10 years over long periods.

The Power of Starting Early

Time is the most powerful variable in compound interest. Consider two investors: Alex starts investing £200 per month at age 25 and stops at 35 — investing for just 10 years. Sam starts at 35 and invests £200 per month continuously until age 65 — investing for 30 years. Assuming 7% annual compound growth, Alex ends up with more money at 65 despite investing for a third of the time, because the 10 extra years of compounding from age 25-35 create a larger base that grows for 30 additional years.

Each year of delay in starting to save or invest has an exponentially larger cost than it appears, because that year's contributions would have compounded for the entire remaining investment period. Starting at 25 versus 35 is not a 10-year difference in outcome — it is often a 2-3x difference in final balance.

Compound Interest Working Against You

Compound interest is equally powerful when you are the borrower. Credit card balances, personal loans and mortgages all use compound interest — meaning unpaid interest is added to the balance and then attracts further interest. A £5,000 credit card balance at 20% APR left unpaid for 5 years grows to approximately £12,442 through compounding alone.

In Australia, Canada, the UK, Singapore and the UAE, credit cards typically carry rates from 15% to 30% APR. Financial advisers consistently recommend paying off high-interest debt before beginning to invest — paying off 20% APR credit card debt is mathematically equivalent to earning a guaranteed 20% annual return on an investment, which no investment consistently achieves with certainty.

Tax-Advantaged Compound Growth

Using tax-advantaged accounts amplifies the compound interest effect by removing the tax drag that would otherwise reduce your effective return each year. In the UK, ISAs (Individual Savings Accounts) allow up to £20,000 per year to grow free of income tax and capital gains tax. In Australia, superannuation contributions compound within a concessional tax environment. In the US, 401(k) and Roth IRA accounts offer tax-advantaged compound growth. In Singapore, the Supplementary Retirement Scheme (SRS) provides tax relief on contributions.

The mathematical benefit of tax-free compounding is substantial. At 7% annual growth over 30 years, £10,000 grows to £76,123. With a 20% annual tax on gains, the effective after-tax growth rate drops and the final balance falls significantly — illustrating why maximising tax-advantaged contributions is one of the most impactful financial decisions available to savers globally.

⚠️ This guide is for educational purposes only and does not constitute financial advice. Investment returns are not guaranteed and past performance does not predict future results. Always seek independent financial advice from a qualified adviser before making investment decisions. ToolBullet and Isometric Ltd are not authorised or regulated by the FCA, SEC, ASIC, MAS or any other financial regulatory body.