What is compound interest? A simple guide with examples

What "interest on interest" actually means

Compound interest is interest calculated not only on the money you put in, but also on the interest that money has already earned.

The difference sounds small in a sentence and is enormous over thirty years. With simple interest, €1,000 at 5% earns €50 every year, always the same: the base never changes. With compound interest, the first year's €50 is added to the capital, so the second year's 5% is calculated on €1,050 and earns €52.50. The third year, on €1,102.50. Each period starts from a slightly larger base than the last.

That is the whole mechanism. There is nothing more sophisticated behind it, and yet it is the reason the term matters so much in any savings plan. If you want the two curves side by side, they are in simple versus compound interest.

Why growth accelerates

The practical consequence is that growth is not linear. In the early years, almost all of the balance is money you contributed. In the final years, most of it is interest.

With €1,000 to start, €100 a month and a 5% annual rate:

• after 10 years, roughly €17,175, of which €13,000 is your own contributions
• after 20 years, roughly €43,816, with €25,000 contributed
• after 30 years, roughly €87,694, with €37,000 contributed

Look at that last stretch: more than half the final value is interest, not your money. And the ten years from year twenty to year thirty add more than the first twenty combined.

There is a precise moment when that flips, and it comes late: on these numbers, accumulated interest does not overtake accumulated contributions until month 294, around year 24 and a half. For almost a quarter of a century the balance is mostly your own money. That is why many people give up before the end: the effect they were promised is only fully visible once the term has already done nearly all the work.

The formula, and what each part does

With regular contributions and monthly compounding:

FV = C·(1+i)ⁿ + A·((1+i)ⁿ − 1)/i

• C is the starting capital
• A is each month's contribution
• i is the annual rate divided by 12
• n is the number of months

The first term is what your starting capital does on its own. The second is what your contributions do, each one compounding for however long it has left. The first month's contribution works for thirty years; the last month's, for none. That is the same idea again, seen from another angle.

Compounding more often helps, but far less than it sounds

"The more frequent the compounding, the better" is repeated everywhere and it is true, but rarely with the figure attached. At a 5% nominal annual rate, this is what each frequency is worth:

Going from annual to monthly adds 0.1162 points. Going from monthly to daily adds one hundredth of a point, and from there to the mathematical limit, which is e raised to 0.05 minus 1, there is essentially nothing left. Frequency matters at the start and exhausts itself immediately; the term and the rate never do. When a product advertises "daily compounding", that is what it is promising over a monthly one.

In Spain compound interest has a legal name: the TAE

This is the part almost no article on compound interest covers, and it is the part that lets you compare real offers.

Because interest can be credited once a year, four times or twelve, two products with the same nominal rate do not return the same thing. To make them comparable, Spanish banking rules require a second figure to be published. Rule thirteen, paragraph 2, of Banco de España Circular 5/2012 defines the tasa anual equivalente as the rate that "at any date equates the present value of the amounts handed over and received over the life of the transaction", calculated with the formula in annex 7 of the same circular.

In plain terms: the TAE is compound interest written into law. The TIN is the nominal rate and says nothing about how often interest is credited; the TAE already carries that frequency, and fees with it. A deposit at 3.00% TIN credited monthly has a TAE of 3.042%; the same 3.00% TIN credited quarterly gives 3.034%; credited once a year, the TAE is exactly 3.00%. The conversion both ways is in the TAE and TIN calculator.

Two details of that rule are worth knowing:

• Annex 7 fixes a standardised month at 30.41666 days, that is 365/12, whether or not the year is a leap year. It is why two banks doing the calculation properly land on the same number.
• For fixed-term deposits of under a year that roll over automatically at a different rate, paragraph 8.4 requires the TAE to take both rates into account, assuming the balance stays for a full year. The TAE on a six-month deposit already contains a reinvestment assumption: it is an annual figure, not what you will collect in six months.

What the TAE does not deduct: the 19% withholding

The same rule is explicit about what does not go into the TAE. Paragraph 8.1 requires the calculation to use "the gross amount of the interest credited, without taking into account tax withheld from the recipient or any tax relief they may benefit from".

That paragraph 8.1 is only one of the rules deciding what goes into the TAE and what does not; the full list, arrangement fees and notary costs included, is in TAE vs TIN in Spain.

And the withholding is real: article 101.4 of Law 35/2006 on personal income tax (IRPF) sets the withholding rate on investment income at 19%, and deposit or account interest is investment income under article 25.2 of the same law.

That has a direct effect on compounding, because what is withheld no longer compounds. A deposit crediting interest annually at 3% TAE leaves 3% × 0.81 = 2.43% effective in your account. On €10,000 over twenty years:

• with no tax at all, €18,061.11
• withholding 19% at each annual credit, €16,163.80

The advertised TAE is the first figure. The second is what reaches your account.

How much tax, and above all when

Savings income is not taxed at your salary rate. It goes into the savings base, on its own scale made up of the state half in article 66.1 and the regional half in article 76 of the IRPF law:

That top band was 28% until 2024. The seventh final provision of Law 7/2024 raised it to 30% with effect from 1 January 2025, amending both articles at once. Any guide written before that date still says 28%.

But for compounding the decisive thing is not the rate, it is the timing. Article 14.1.a) of the same law assigns investment income "to the tax period in which it is due and payable to the recipient". Not when it is generated: when it can be demanded. A deposit that pays only at maturity produces nothing payable until then, so it compounds in full and is taxed once. That is exactly what happens with a Spanish Treasury bill, which pays no interim coupon: the entire return becomes payable on the redemption date.

Why a fund compounds differently from a deposit

Article 94.1.a) of the IRPF law contains the most powerful version of this idea in Spanish law. Where an investment fund is redeemed and the proceeds are used to subscribe units in another collective investment undertaking, "no capital gain or loss shall be computed", and the new units keep the value and the acquisition date of the old ones.

In other words, switching funds does not interrupt compounding: there is no settlement, no tax, and the capital carries on compounding in full until you genuinely redeem.

With two limits worth keeping in view:

• It does not apply to exchange-traded funds. Article 3.5 of Law 11/2021 expressly removed units in listed investment funds, and shares in listed companies of the same kind, from the deferral regime with effect from 1 January 2022. Two products that look very similar from the outside behave in opposite ways on this point.
• It is a deferral, not an exemption. The tax is paid in full at the end, on an accumulated gain that may well cross into a higher band of the savings scale.

None of this says which product suits you, which depends on fees, risk and horizon, and this page assesses none of them. It only explains why two wrappers with the same gross return can leave you with different amounts.

A worked example with real numbers

€10,000, a 3% gross return, twenty years, and the same person in both cases, with no other savings income adding to their base.

Case A, annual crediting with withholding. Interest is credited each year and 19% is withheld. The capital compounds at 2.43%. After twenty years: €16,163.80.

Case B, everything deferred to the end. Nothing is settled along the way, so the capital compounds at the full 3% and reaches €18,061.11. The gain is €8,061.11, taxed entirely in a single tax year: the first €6,000 at 19% (€1,140) and the remaining €2,061.11 at 21% (€432.83), €1,572.83 in total. That leaves €16,488.28.

A difference of €324.48, and here is the interesting part: case B pays a higher average rate (19.51% against case A's 19%), because bunching twenty years of return into one tax year pushes part of the gain into the second band. It still wins, because for twenty years it compounded on a larger balance. When the tax is paid matters more than the rate at which it is paid.

You can reproduce the compounding side with your own numbers in the compound interest calculator.

The rule of 72, and where it stops working

A useful shortcut for a rough figure without a calculator: divide 72 by the annual rate as a percentage, and you get approximately the number of years for money to double.

It is an approximation, and it is worth knowing which way it errs. The exact value is ln 2 / ln(1+r):

The rule is exact at around 8%, too optimistic below it and too pessimistic above. In the 4% to 10% band, where almost every real savings decision falls, the error is under a year and the shortcut holds. At 1% it is out by more than two years, and at double-digit rates it stops being useful.

Inflation is deducted by dividing, not subtracting

€87,694 in thirty years does not buy what it buys today. At 2% average inflation, that amount is worth roughly €48,400 in today's terms. The return that matters is the real one.

And it is worked out by dividing, not subtracting: (1 + nominal) / (1 + inflation) − 1. At 5% nominal against 2% inflation the answer is 2.941%, not the 3.000% subtraction gives. The gap is small over one year and is not small over thirty, because it compounds too. You can see the effect on a specific amount in the inflation calculator, and if you want the concept before the tool, inflation in Spain covers how it is measured and how much buying power Spanish prices have really taken since 2021.

And working against you

The same mechanism applies to debt. Unpaid credit-card interest is added to the balance and starts earning interest itself, exactly as in savings, only in the opposite direction, and usually at much higher rates.

€2,000 at a 20% TAE, with nothing repaid, becomes €4,976.64 in five years. And here there is no withholding slowing the compounding down and no article of the IRPF deferring it: interest on debt compounds in full and without pause. That is why paying off expensive debt is often the best guaranteed return available to you.