See how your savings or investments grow over time with the power of compound interest. Adjust the starting amount, interest rate, time period and compounding frequency to model different scenarios.
Compound interest means you earn interest on your interest as well as your original principal. This creates exponential growth over time — the longer your money is invested, the more dramatic the effect becomes.
A = P(1 + r/n)^(nt) where: A = final amount, P = principal (starting amount), r = annual interest rate as a decimal, n = number of times interest compounds per year, t = number of years.
£10,000 invested at 7% annually for 20 years grows to approximately £38,697. The same amount invested for 30 years grows to £76,123. An extra 10 years nearly doubles your money. This is why financial advisers always stress starting to invest as early as possible.
The more frequently interest compounds, the faster your money grows. Daily compounding slightly outperforms annual compounding, though the difference is small at typical interest rates.
Simple interest pays you a fixed amount based only on your original principal each year. £10,000 at 5% simple interest earns £500 every year: year 1 = £500, year 2 = £500, year 3 = £500, totaling £1,500 after 3 years. Compound interest pays you interest on your growing balance including previously earned interest. The same £10,000 at 5% compounded annually earns £500 in year 1 (balance now £10,500), £525 in year 2 (5% of £10,500), £551.25 in year 3, totaling £1,576.25 — £76.25 more. Over longer periods the difference becomes enormous: after 30 years, simple interest delivers £15,000 total (£5,000 interest) whilst compound interest delivers £43,219 (£33,219 interest) — more than six times the interest. This exponential growth is why Einstein allegedly called compound interest "the eighth wonder of the world." Most savings accounts, investments and loans use compound interest, though some promotional savings deals or bonds use simple interest which looks attractive short-term but underperforms long-term. When comparing financial products, always check whether interest compounds and how frequently.
Compound growth is exponential not linear, meaning returns accelerate dramatically in later years. Consider £10,000 invested at 7% annually: after 10 years you have £19,672. After 20 years (just 10 more years) you have £38,697 — nearly double your 10-year result. After 30 years you have £76,123 — nearly double again. Most of your final wealth comes from the last decade of investing, but you can only access those final decades by starting early. Someone who invests £10,000 at age 25 has £149,745 at age 65 (40 years). Someone who waits until age 35 has only £76,123 (30 years) — half the result despite investing the same amount, just 10 years later. This is why financial advisers obsess over starting early even if you can only invest small amounts. £100 monthly from age 25 to 65 at 7% grows to £262,481. Starting at 35 yields only £122,709. The decade from 25-35 matters more than the next three decades combined because those early contributions have longest to compound. Many people delay investing thinking they'll invest more later when they earn more, but this usually backfires — you rarely catch up by investing more later. Start now with whatever you can afford, even £50 monthly, rather than waiting for "the right time" with more money.
Time invested matters more than rate for most people, though both are important. Increasing your time horizon from 20 to 30 years typically has more impact than increasing returns from 6% to 7%. However, small rate differences compound significantly: £100,000 growing at 6% for 30 years becomes £574,349, whilst 7% yields £761,226 — a £186,877 difference from just 1% extra annual return. This is why investment fees matter so much: a fund charging 1.5% annual fees versus 0.5% might have identical stated returns, but after fees you earn 5.5% versus 6.5% — costing you tens of thousands over decades. Focus on both: maximize time by starting immediately regardless of age, and maximize returns by minimizing fees, diversifying appropriately, and staying invested through market volatility rather than panic selling in downturns. For young investors time is their superpower making rate differences less critical — a 25-year-old can accept slightly lower guaranteed returns because they have 40 years for compounding. Older investors need higher returns to compensate for shorter time horizons, though this often means accepting more risk. The worst mistake is delaying investment while seeking perfect rates — a 6% return starting today beats waiting two years for 7% because you lose two years of compounding that can never be recovered.
Using A = P(1 + r/n)^(nt): A = 5,000(1 + 0.05/12)^(12×10) = 5,000(1.00417)^120 = £8,235. Interest earned = £8,235 − £5,000 = £3,235. Total return = 64.7%. More than half your final balance comes from interest, not principal.
A = 10,000(1 + 0.07/1)^(1×20) = 10,000(1.07)^20 = £38,697. Interest earned = £28,697. Nearly tripling your money. If compounded daily instead of annually: £40,218 — £1,521 extra from more frequent compounding.
A = 50,000(1 + 0.06/4)^(4×30) = 50,000(1.015)^120 = £301,427. Interest earned = £251,427. Your initial £50,000 contribution becomes £301,427 — over six times your money. This demonstrates the extraordinary power of multi-decade compounding.
Start investing as early as possible, even if amounts are tiny — £50 monthly beats £200 monthly started later due to the time advantage. Make regular contributions if possible as pound-cost averaging buys more shares when prices are low, smoothing volatility. Reinvest dividends and interest rather than spending them to maintain exponential growth. Minimize fees ruthlessly as 1-2% annual charges dramatically reduce long-term wealth — use low-cost index funds rather than expensive actively-managed funds. Stay invested through market downturns as selling locks in losses and misses recovery gains that follow crashes. Consider tax-efficient accounts like ISAs and pensions which protect compounding from tax drag — paying 20% tax annually on gains significantly reduces compounding power over decades. Avoid withdrawing from investments early as you lose not just the withdrawn amount but all future compounding on that money. Increase contributions when you get raises rather than lifestyle inflation — directing pay rises to investments supercharges compounding. Understand that compound returns aren't guaranteed: stock markets average 7-10% long-term but vary hugely year-to-year with some years negative. Bonds offer more stable but lower returns around 3-5%. Savings accounts currently 4-5% are safe but inflation erodes real purchasing power. Diversify across assets and geographies to balance growth potential with risk management. Most importantly, remember that compound interest works against you with debt: credit card balances at 18% APR double every 4 years if unpaid, so prioritize clearing high-interest debt before investing aggressively. The mathematics of compounding is neutral — it amplifies both wealth building and debt growth exponentially.