Compound Interest Calculator
Enter a starting amount, a regular contribution and a rate to see how a balance grows. The chart separates what you paid in from what the money earned, so the shape of compounding is visible rather than implied.
Set to 0 for a lump sum left alone
A = P(1+r/n)^(nt) + C·[((1+r/n)^(nt)−1)/(r/n)] where P=10000, C=250, r=7%, n=12, t=20| Year | Paid in | Growth | Balance |
|---|---|---|---|
| 1 | $13,000.00 | $821.05 | $13,821.05 |
| 2 | $16,000.00 | $1,918.32 | $17,918.32 |
| 3 | $19,000.00 | $3,311.78 | $22,311.78 |
| 4 | $22,000.00 | $5,022.85 | $27,022.85 |
| 5 | $25,000.00 | $7,074.48 | $32,074.48 |
| 6 | $28,000.00 | $9,491.29 | $37,491.29 |
| 7 | $31,000.00 | $12,299.69 | $43,299.69 |
| 8 | $34,000.00 | $15,527.97 | $49,527.97 |
| 9 | $37,000.00 | $19,206.50 | $56,206.50 |
| 10 | $40,000.00 | $23,367.82 | $63,367.82 |
A projection, not a forecast. It assumes a fixed return every single period, which no real investment delivers — markets fall as well as rise, and the order those years arrive in changes the outcome. It also ignores inflation, tax, platform fees and fund charges, all of which come out of the figure above. Treat it as the arithmetic of compounding, and nothing more. This is not financial advice.
Calculated in your browser. Your savings figures never leave your device.
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How to use the compound interest calculator
- Enter your starting amount — a lump sum you already hold, or zero if you are beginning from nothing.
- Set the regular contribution added each compounding period, or leave it at zero to model a lump sum left alone.
- Enter the annual return you want to assume, and how many years to project.
- Choose the compounding frequency — monthly matches most savings accounts and investment platforms.
- Read the chart. The lower band is what you paid in; the upper band is growth. Where the upper band overtakes the lower one is the crossover year.
Nothing is uploaded. The projection runs entirely in your browser.
What compounding actually is
Compound interest means the interest earns interest.
That sentence sounds like a technicality and behaves like a force of nature. Simple interest on £1,000 at 5% pays £50 a year, every year, unchanged. Compound interest pays £50 in the first year, then charges the second year's 5% against £1,050, giving £52.50, then against £1,102.50, giving £55.13. Each year's earnings are slightly larger than the last, because the base they are calculated on keeps growing.
Over short periods the difference is trivial. Over long ones it is the entire story. Left alone for thirty years at 5%, simple interest turns £1,000 into £2,500. Compound interest turns it into £4,322. Extend it to fifty years and the gap widens to £3,500 against £11,467.
What makes this counter-intuitive is that human intuition is linear. We are good at extrapolating straight lines and bad at extrapolating curves, so a growth rate that seems modest early on produces a result that feels implausible later — even though nothing surprising happened in any individual year.
The formula
For a lump sum:
A = P(1 + r/n)^(nt)
where P is the starting amount, r the annual rate as a decimal, n the compounding periods per year and t the number of years.
With regular contributions, a second term is added — the future value of a series of equal payments:
A = P(1 + r/n)^(nt) + C · [((1 + r/n)^(nt) − 1) / (r/n)]
where C is the contribution made at the end of each period.
The second expression looks worse than it is. Each contribution compounds for however many periods remain after it is deposited: the first one compounds almost the full term, the last one not at all. Summing that geometric series gives the bracket above. The calculator shows whichever formula applies to your inputs, with your numbers substituted in.
Frequency matters less than you think
Compounding daily instead of yearly sounds like it should be a meaningful upgrade. It is not.
£1,000 at 10% over ten years:
| Compounded | Final balance |
|---|---|
| Yearly | £2,593.74 |
| Half-yearly | £2,653.30 |
| Quarterly | £2,685.06 |
| Monthly | £2,707.04 |
| Daily | £2,717.91 |
Yearly to monthly gains £113. Monthly to daily gains £11. Each step buys less than the one before, because the sequence is converging on the continuous-compounding limit of £2,718.28 — which is 1,000 × e, and no amount of extra frequency gets past it.
The lesson is where to direct attention. A product advertising daily compounding at 4% is worse than one compounding yearly at 4.5%. The rate and the time horizon are the variables that move the outcome; frequency is a detail worth checking and not worth chasing.
Where frequency does matter is comparison. The effective annual rate — (1 + r/n)ⁿ − 1 — converts any nominal rate and frequency into a single comparable number, and it is shown alongside your result for exactly that reason.
The crossover, and why time beats amount
The chart on this page stacks contributions below growth, and the point where growth overtakes contributions is the most informative thing on it.
For a typical long-horizon scenario — a modest starting balance, steady monthly contributions, a mid-single-digit return — the crossover lands somewhere in the second decade. Before it, the account is essentially a savings jar with a bonus. After it, most of the balance exists because of returns rather than deposits, and the account grows faster each year without you doing anything differently.
This is why starting early beats contributing more. Money added in year one has the entire term to compound; money added in year twenty has whatever is left. The same total contribution produces a very different result depending on when it went in, and no amount of later effort fully recovers an early delay.
You can see this directly: run the calculator over thirty years, then over twenty with a proportionally larger contribution so the total paid in matches. The thirty-year version wins, usually by a wide margin.
What this calculator leaves out
Inflation. All figures are nominal. At 3% inflation, money loses roughly half its purchasing power every 24 years. Enter your return minus expected inflation to see results in today's money.
Tax. Interest, dividends and capital gains are taxable in most jurisdictions unless held in a sheltered account. Tax paid along the way reduces the base that compounds, which costs more than the tax itself.
Fees. Platform charges and fund fees come out of returns. A 1% annual fee against a 7% return removes far more than a seventh of the final balance, because the fee compounds against you for the whole term.
Volatility. A fixed return every period is a smooth line that no real market draws. The same average return delivered in a different order produces a different result when money is being withdrawn.
Compounding runs the other way too
The identical formula governs debt. A credit card at 22% compounding monthly has an effective annual rate near 24.4%, and a balance left untouched grows on exactly the curve described above — just pointing at you instead of for you.
This is why paying down high-interest debt is usually a better return than investing. A guaranteed 22% saved is a better outcome than a hoped-for 7% earned, with none of the risk. Run both sides through this calculator and the comparison is stark.
Privacy: how this tool handles your figures
Everything runs in your browser. Your starting balance, contributions, target and time horizon are never transmitted, logged or stored, and closing the tab discards them.
Taken together those inputs are a financial profile: how much you have, how much you can save each month, and what you are aiming at. That combination is precisely what makes someone a valuable prospect to a firm selling investment products, which is why so many compounding calculators sit behind an email capture or belong to a company with something to sell.
The formula is a handful of multiplications. You can confirm nothing leaves by opening developer tools and watching the Network tab, or by disconnecting from the internet after the page loads — the calculator carries on working, because it never needed anything else.
Frequently asked questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the original amount, so £1,000 at 5% earns £50 every year forever. Compound interest is calculated on the original amount plus everything it has already earned, so the second year earns 5% of £1,050, the third year 5% of £1,102.50, and so on. Over one year the two are identical. Over thirty years, simple interest turns £1,000 into £2,500 while compound interest turns it into £4,322. The whole difference is that compounding lets the earnings earn.
Does compounding more often make a big difference?
Less than most people assume. £1,000 at 10% for ten years becomes £2,594 compounded yearly, £2,707 compounded monthly, and £2,718 compounded daily. Going from yearly to monthly gains about £113; going from monthly to daily gains about £11. The returns diminish quickly because you are converging on a mathematical ceiling — continuous compounding, which is the limit as the frequency approaches infinity. The rate and the number of years matter enormously; the frequency is a rounding detail by comparison.
What is the effective annual rate?
It is what a rate actually delivers once compounding is accounted for, which lets you compare offers quoted at different frequencies. A nominal 12% compounded monthly is not 12% a year — each month adds 1%, and twelve months of that gives 12.68%. That 12.68% is the effective annual rate. Savings products often advertise it as AER or APY. Whenever two products quote different compounding frequencies, the effective rate is the only fair comparison.
Does this account for inflation?
No, and that matters. Every figure here is nominal — the number of currency units you will hold, not what those units will buy. If the calculator projects a balance of £500,000 in thirty years and inflation averages 3%, that sum has roughly the purchasing power of £206,000 today. A rough way to see the real picture is to enter your expected return minus expected inflation instead of the nominal return: the result is then in today's money.
What is the rule of 72?
A mental shortcut for how long money takes to double: divide 72 by the annual percentage rate. At 6% that is 12 years, at 8% it is 9 years, at 12% it is 6 years. It is an approximation that is closest between about 6% and 10% and drifts at the extremes, but it is accurate enough to sanity-check a projection in your head. It also works in reverse — if something claims to double your money in three years, it is claiming roughly 24% a year, which is a useful thing to notice.
Why does the chart cross over partway through?
The chart stacks what you paid in underneath what the money earned. Early on, contributions dominate — the balance is mostly your own deposits. At some point the accumulated growth exceeds the accumulated contributions, and from then on the account is being driven more by returns than by anything you add. That crossover year is the single clearest illustration of what compounding actually does, and it is why time in the market is discussed more than the amount invested.
Is a fixed annual return realistic?
No. No investment delivers the same return every year, and this calculator assumes exactly that. Real markets fall as well as rise, and the order in which good and bad years arrive changes the outcome — particularly if you are withdrawing rather than accumulating. Treat the result as the arithmetic of compounding under a smooth assumption, which is useful for understanding the mechanism and comparing scenarios, not as a prediction of any real account.
Are my figures sent anywhere?
No. The projection runs in your browser and nothing is transmitted, logged or stored. Your savings balance, your monthly contribution and your target are a detailed financial profile, and they are exactly what makes a person valuable to a firm selling investment products. There is no reason for a compounding formula to require a server, so this one does not use one.