How Compound Interest Works
Compound interest is the process of earning interest on both your original investment (the principal) and on the interest you have already earned. Unlike simple interest — which only applies to the original amount — compound interest causes wealth to grow exponentially because each year's returns are reinvested and generate their own returns.
This exponential effect is what makes starting early so powerful. A £10,000 investment at 8% annual return grows to £21,589 after 10 years without any additional contributions. After 30 years it becomes £100,627 — a 10x multiple on the original investment. The same amount with simple interest would only reach £34,000 after 30 years — less than a third of the compound result.
The Compound Interest Formula
The standard formula for compound interest is:
A = P × (1 + r/n)^(n×t)
A = Final amount | P = Principal | r = Annual rate (decimal)
n = Compounding periods per year | t = Years
When you add regular monthly contributions, each deposit also compounds over its remaining time in the investment. Early contributions have the longest time to compound and contribute disproportionately to the final balance — which is why consistency beats timing for long-term wealth building.
The Rule of 72
A quick mental shortcut: divide 72 by your annual return rate to estimate how many years it takes to double your money. At 8% per year, money doubles in approximately 9 years. At 10%, roughly 7.2 years. At 6%, about 12 years. Even a 2% difference in annual return has an enormous effect over 20-30 year time horizons due to the exponential nature of compound growth.
Historical Investment Return Rates
~10%
S&P 500
(historical avg)
7–8%
Diversified
stock portfolio
1–5%
High-yield
savings account
Variable
Crypto
(high risk)
Past performance does not guarantee future results. Return rates are illustrative only. Higher projected returns typically involve significantly higher risk.
How Monthly Contributions Amplify Growth
Regular monthly contributions compound the effect of compound interest in two ways. First, each deposit immediately starts earning returns. Second, contributions made early compound for the longest time and contribute disproportionately to the final balance. A regular £500 per month contribution at 8% over 20 years produces a final balance far exceeding the £120,000 contributed in cash. This is the mathematical foundation of strategies like dollar-cost averaging and systematic investing.
If you are actively trading crypto, use the position size calculator to manage risk on individual trades — and this calculator to model the long-term compound growth of capital you are not actively trading.
Common Questions About Compound Interest
What is compound interest?
Compound interest is interest calculated on both your original principal and all interest already earned. Each period's returns are reinvested, so subsequent periods calculate returns on a progressively larger base. This creates exponential growth — the longer the investment period, the more powerful the compounding effect becomes.
What is the compound interest formula?
The basic formula is A = P(1 + r/n)^(nt), where A is the final amount, P is your starting 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 investments with regular monthly contributions, the formula extends to sum the compound growth of each individual contribution over its remaining time — which is what this calculator computes.
What annual return rate should I use in the calculator?
The S&P 500 has historically returned approximately 10% per year before inflation, or 7–8% adjusted for inflation. A diversified stock portfolio is typically modelled at 7–10%. Bonds average 3–5%. High-yield savings accounts currently offer 1–5% depending on rate conditions. Use the quick preset buttons in the calculator to compare scenarios side by side. Past performance does not guarantee future results.
How do monthly contributions affect the final balance?
Monthly contributions dramatically accelerate compound growth because each new deposit immediately begins compounding. Early contributions benefit from the longest compound period and have an outsized impact on the final total. A regular £500/month at 8% over 20 years produces a final balance far exceeding the £120,000 cash contributed — because those early deposits compound for many years. This is the mathematical basis of systematic investing strategies.
What is the Rule of 72?
The Rule of 72 is a quick mental shortcut: divide 72 by your annual return rate to estimate how long it takes to double your money. At 8% per year, money doubles in roughly 9 years (72 ÷ 8). At 10% it takes about 7.2 years. At 6%, roughly 12 years. It is a useful check when comparing return scenarios in this calculator — small differences in rate produce very large differences in final balance over 20-30 year periods.
What is the difference between compound and simple interest?
Simple interest only applies to the original principal — a £10,000 investment at 8% simple interest always earns £800 per year. Compound interest reinvests those gains: in year 2 you earn interest on £10,800, in year 3 on £11,664, and so on. Over 30 years, £10,000 at 8% simple interest reaches £34,000. The same investment compounded reaches over £100,000 — nearly three times more — purely from reinvesting the gains.