Compound interest
Compound interest is the growth loop at the heart of saving and borrowing: each time interest is added to a balance, the next round of interest is worked out on that new, bigger balance, so the money begins feeding its own growth. The gains look almost identical at first and then pull apart — an account that adds €50 in its first year is adding noticeably more every year after, without another cent deposited. That loop is the engine behind long-term savings, pensions and most investment growth, and, pointed the other way, it is how debt balloons when left unpaid.
The core idea
Watch one balance closely and the whole mechanism is visible. €1,000 in an account paying 5% compounded once a year becomes €1,050.00 after year one, €1,102.50 after year two, €1,157.63 after year three. Year two’s gain of €52.50 beat year one’s €50 because by then the €50 itself had joined the workforce. Run the same account for ten years and it reaches €1,628.89 — while simple interest, which pays on the starting €1,000 forever and ignores everything since, would still be plodding along at a flat €50 a year towards €1,500.00.
Why time is the dominant ingredient
Because each period builds on the last, the effect is small at first and then grows sharply, so most of the gain arrives in the later years. Time, not the size of your first deposit, does the heavy lifting. Put away €100 a month at 5% for 30 years and you finish with €83,226 — you paid in €36,000, and the other €47,226 is compound interest. The rate matters enormously over that span: at 3% the same habit grows to €58,274, at 7% to €121,997, of which €85,997 is interest. The Rule of 72 gives a quick feel for the pace — divide 72 by the rate to estimate the years a balance takes to double.
Compounding cuts both ways. Inflation compounds against your savings, shrinking what your money can buy, so the headline rate is never the whole story. When comparing products, the AER (annual equivalent rate) shows the true yearly return once compounding is counted, and APR does the same for the cost of borrowing.
What you can do from here
From this page you can run your own numbers in the calculator — a principal, a rate, a timeframe and a monthly contribution — and watch the balance grow year by year. You can read the guides that explain the mechanics step by step, compare compound interest directly against simple interest, and walk through worked examples that show the arithmetic in full, so the figures above are ones you can check rather than trust.
For decisions with real money at stake, this page explains the mechanics; a qualified adviser handles what is right for your own circumstances.
Last reviewed 7 July 2026
Calculate it
Understand it
A plain explanation of compound interest, why it accelerates, and why it matters for anyone saving or borrowing.
Guide How compound interest worksThe four moving parts — principal, rate, frequency and time — and how each one changes what you end up with.
Guide Percentage change, explainedHow percentage increase and decrease work, why the direction matters, and why a fall needs a bigger rise to undo it.
Guide The Rule of 72A mental shortcut for how long money takes to double — how it works, how accurate it is, and where it breaks down.
Guide Why compound interest makes pensions workHow decades of compounding do most of the work in a pension, and why starting earlier beats contributing more.
Guide When compound interest works against youCompounding applies to what you owe as well as what you save — credit cards, loans and how to read APR.
Guide The compound interest formula, explainedWhat FV = P(1 + r/n)^(nt) actually says, term by term, with a worked calculation you can follow.
Guide How inflation compoundsInflation is compound interest pointed at prices: the same loop, running against your money instead of for it.
Guide Compound interest and inflation: real returnsWhy the growth you see is not the growth you get, and how to think about returns after inflation.
Guide Saving monthly vs investing a lump sumWhich builds more: steady monthly saving or a one-off lump sum? The honest maths on both.
Guide How tax affects compound interestInterest is usually taxable, and tax paid along the way compounds too. How to think about returns after tax, with Ireland’s DIRT as a worked case.
Guide Common compound interest mistakesThe misunderstandings that quietly cost savers money — and how to avoid each one.
GuideCompare
The two ways interest can be calculated, how far apart they end up, and which one you are actually being offered.
Comparison Monthly vs annual compoundingHow much compounding frequency really matters, with the honest answer: less than most people expect.
ComparisonSee it in numbers
A worked example of steady small saving: what €100 a month becomes over 30 years at different rates.
Example A €10,000 lump sum left for 20 yearsWhat happens when you invest once and leave it alone — €10,000 over 20 years at different rates.
Example Starting at 25 vs starting at 35Ten years’ head start, same monthly saving: the gap at retirement is bigger than most people guess.
Example How fast money doubles at different ratesExact doubling times from 1% to 12%, side by side with the Rule of 72 estimate.
ExampleKey terms
Follow the rabbit hole
One idea leads to the next. Start anywhere.
- What is compound interest?A plain explanation of compound interest, why it accelerates, and why it matters for anyone saving or borrowing.
- How compound interest worksThe four moving parts — principal, rate, frequency and time — and how each one changes what you end up with.
- The compound interest formula, explainedWhat FV = P(1 + r/n)^(nt) actually says, term by term, with a worked calculation you can follow.
- The Rule of 72A mental shortcut for how long money takes to double — how it works, how accurate it is, and where it breaks down.
- Compound interest and inflation: real returnsWhy the growth you see is not the growth you get, and how to think about returns after inflation.
- Why compound interest makes pensions workHow decades of compounding do most of the work in a pension, and why starting earlier beats contributing more.
Questions people ask
Did Einstein really call compound interest the eighth wonder of the world?
There is no credible evidence Einstein said it. Researchers at Quote Investigator traced the "eighth wonder of the world" attribution and found it appearing decades after his death, with no source in his own writings. Treat it as apocryphal: the maths is impressive enough without the celebrity endorsement.
What is a realistic interest rate to assume?
It depends entirely on what the money is in: deposit accounts, bonds and shares behave differently, and Around doesn't predict markets. Our worked examples use a 3% to 7% range purely to show how the maths responds to different rates.
Do regular contributions earn compound interest too?
Yes: every contribution starts its own compounding clock the moment it lands. That's why steady monthly saving builds so much more than the deposits alone: €100 a month for 30 years at 5% becomes €83,226, of which only €36,000 was paid in.
How long does it take to double your money?
Divide 72 by the annual rate for a quick estimate: at 6%, that's roughly 12 years, and the exact figure is 11.9. The estimate is reliable for ordinary rates and only drifts off at extremes.
Does inflation cancel out compound interest?
It offsets part of it, not all of it. Growth in euros (nominal) and growth in buying power (real) are different: roughly, the real return equals the rate minus inflation. At 5% growth with 2% inflation, the real rate is about 2.94%.
Does compound interest apply to debt?
Yes. Unpaid interest is added to the balance and then earns interest itself, the same acceleration that grows savings grows debt. Credit cards are the everyday example.
Is compound interest taxed?
Usually yes: interest is taxable income in most countries. In Ireland, deposit interest is subject to DIRT at 33%, the rate published by Revenue as of this review. Rules and rates vary by country and circumstance, so official tax guidance is the source of truth.
Is simple interest still used anywhere?
Mostly no: savings, pensions, mortgages and cards all compound. Simple-interest calculations survive in some short-term lending arrangements and in how certain bond payments are quoted, but compound interest is the default assumption to carry.
How often do banks compound interest?
It varies by account and bank; monthly and yearly are both common. The honest way to compare accounts is the AER, which folds compounding frequency into a single rate.
Is monthly compounding better than annual?
Monthly, slightly, at the same nominal rate: on €10,000 at 5% over 10 years, monthly compounding beats annual by €181.14. It's a real but small difference, and rate and time matter far more. AER lets you compare accounts fairly regardless of how often they compound.
What is the difference between APR and AER?
APR describes the yearly cost of borrowing, including standard charges. AER describes what savings genuinely pay once compounding frequency is included. One prices debt, the other prices saving.
Is it worth saving small amounts?
Yes, if there's time for it to work. €100 a month at 5% for 30 years becomes €83,226, of which €47,226 is interest. Small amounts aren't small once they've had decades to compound.
Can something increase by more than 100%?
An increase has no upper limit — something that triples has risen 200%. A decrease is capped, because losing everything means reaching zero and there is nothing left to lose.