Compound Interest Calculator

This compound interest calculator projects capital and monthly contributions, net of fees, in nominal and real terms.

The results displayed are for strictly indicative and educational purposes. They do not constitute investment advice, a personalized recommendation, or an incentive to use any specific financial product.

Compound interest: the principle

Compound interest is the mechanism by which the interest earned on a principal itself earns interest in later periods. Simple interest is computed on the initial principal only; compound interest folds accumulated gains back into the base. Over a long horizon, this is what makes time a more powerful lever than the amount invested. A compound interest calculator still does not predict an outcome: it shows what happens if the assumptions about return, duration and inflation hold, and plots the nominal projection and its real purchasing power.

The calculator settings

At the default setting (€10,000 to start, €200 a month, 7% annual return, 30 years, 2% inflation), the final capital reaches €302,828 in nominal euros, for €82,000 paid in. In today’s money it is worth €167,183: thirty years of 2% inflation take away 45% of its value.

Annual fees. They come off the return, so a 1% annual fee on a 7% return leaves 6% a year. With a 1% fee, the default result falls to €247,175, and the calculator shows what the fees cost: €55,654, more than two thirds of the amount paid in.

Annual or monthly compounding. With annual compounding, interest is added to the capital once a year and the year’s contributions count at year end. With monthly compounding, the annual rate divided by 12 applies every month, and each contribution earns interest from the following month. At the default setting, the final capital goes from €302,828 to €325,159.

Year-by-year table. A collapsible table below the chart gives, for each year, the cumulative amount paid in, cumulative interest, nominal capital and its value in purchasing power. The tipping point shows directly: at the default setting, cumulative interest overtakes the amount paid in from year 17.

The compound interest formula

The calculation rests on a standard formula, used in both personal finance and market analysis:

A = P × (1 + r/n)^n×t

• A = final amount (principal + accumulated interest)
• P = initial principal
• r = annual interest rate (as a decimal: 5% = 0.05)
• n = number of compounding periods per year (1 = annual, 12 = monthly)
• t = duration in years

With annual compounding (n = 1), the formula simplifies to A = P × (1 + r)^t. That is the calculator’s default setting, the version that makes the exponential mechanism easiest to read; the monthly option applies n = 12. Three versions coexist depending on the compounding frequency and on whether contributions are added, the subject of the three formulas and their limits.

Compound interest with monthly contributions: the future value

Regular contributions add a second term. Each payment compounds over the time left until the end date, and these compoundings form a geometric series whose sum is the future value: FV = C × ((1 + i)^N − 1) / i, where C is the contribution, i the rate per period and N the number of payments.

With €200 paid in every month for 30 years at 5%, compounded monthly (i = 0.05 / 12, N = 360), the future value reaches €166,452 for €72,000 paid in. With annual compounding, the calculator counts €2,400 paid in at the end of each year and arrives at €159,453. The final capital adds the two terms: at the default setting, contributions make up three quarters of it (€226,706 out of €302,828), the €10,000 starting capital the rest.

Worked example: €10,000 invested at 5% for 10 years

€10,000 at a 5% annual rate, annual compounding, no extra contributions:

A = 10,000 × (1 + 0.05)¹⁰ = €16,289. The principal generated €6,289 in interest. What makes the mechanism remarkable is how that interest is spread over time: the first year produces €500, the tenth €776. With simple interest, the same investment would have returned exactly €5,000. The €1,289 gap comes solely from interest compounding on itself.

With monthly compounding, the same investment reaches €16,470, or €181 more. Compounded monthly, a 5% rate is equivalent to an effective annual rate of 5.12%.

Capital over 10 years at 5%, year by year

Annual interest rises from €500 to €776 with no extra contribution. Over the last 5 years the capital generates €3,526 of interest, against €2,763 over the first 5: most of the gains concentrate at the end.

Simple vs compound interest: what’s the difference?

Simple interest is computed on the initial principal only: €10,000 at 5% returns €500 every year, indefinitely. Linear growth (I = P × r × t). Compound interest folds prior interest into the base: the second year earns on €10,500. Exponential growth.

The gap widens with every year: €1,289 over 10 years, €18,219 over 30, almost double the initial principal. This is why the investment horizon is, in practice, the most powerful lever over a long period. The same arithmetic runs inside the main investment accounts for children, from custodial to 529, whose horizon stretches from a child’s birth to adulthood.

Why time is the main lever

Exponential growth produces most of its effect in the later periods. Early years contribute modestly; the later years account for the bulk of the gains. The direct consequence: extending the horizon by a few years can sharply reduce the monthly effort needed to reach a goal, while shortening it imposes a disproportionate one. Discipline and regularity of contributions can matter more than the starting amount.

Regularity matters for a reason the formula makes explicit once contributions are added. Each payment compounds over its own remaining horizon. A skipped contribution is not made up by a later one, because it loses the years it would have compounded. A prolonged pause, even a temporary one, shrinks the base on which every later period builds. Regular flows also spread entry points over time, which reduces how much the outcome depends on a handful of discretionary timing decisions. The dispersion of contributions over time and the frequency of interruptions are therefore readable signals of how robust a trajectory is. The assumption has limits of its own, since a liquidity shock or an income constraint can break the flow regardless of intent.

Over thirty years, half the gains arrive in the last third

At 5% a year over thirty years, the last ten years produce half the gains (50%, or 39% of the final capital), the first ten less than a fifth. At 7% over the same horizon, capital is multiplied by about 7.6 and the share of gains formed in the last third reaches 57%. The simulator’s year-by-year table, with the monthly contribution set to 0, shows it. Past the halfway point, duration weighs more than the level of the rate.

Intuition still reads the projection as a straight line. Behavioral finance calls it exponential growth bias: Stango and Zinman (Journal of Finance, 2009) show that households intuitively linearize exponential functions and underestimate the future value of savings, and that the most biased save less and borrow more. A 20- or 30-year horizon gets cut mentally into equal blocks, hence results judged disappointing early on and spectacular in hindsight. The simulator corrects the calculation error, not necessarily the reading error: comparing two points on the curve and extrapolating by eye brings the linear reading back.

The calculator applies a constant annual rate, while real returns arrive in sequence. Years alternating +30% and −20% average +5% but compound at 1.98% a year: €10,000 then grows to about €14,800 over twenty years, against the €26,533 a steady 5% produces. Late concentration has its downside too. A break late in the horizon (volatility, a forced withdrawal, a change in rate regime) hits when accumulated capital is at its highest, and weighs all the more on the final result.

Duration, rate and fees: what the exponent decides

In the formula, the rate sits in the base and duration in the exponent. €10,000 invested at 4% for 30 years reaches €32,434. At 6% for 20 years it reaches €32,071. Ten extra years offset two points of annual return here. Doubling time gives the reason: capital doubles in 17.7 years at 4% and in 11.9 years at 6% (18 and 12 years by the rule of 72). Thirty years at 4% and twenty at 6% both amount to about 1.7 doublings. Hence the weight of the investment horizon in the outcome.

The trade-off is not proportional. Matching 20 years at 6% in only 10 years would take a return of 12.4% a year. Halving the duration requires more than doubling the rate, and the constraint tightens as the horizon shortens. Time cannot close every gap, though: €10,000 at 8% for ten years gives about €21,600, against €18,100 at 3% for twenty.

Fees go through the same exponent, since they come off the rate every year. With a 5% gross return and 1 point of annual fees, €10,000 becomes €21,911 in 20 years instead of €26,533, or 17% less. Over 30 years the gap reaches 25% (€32,434 against €43,219). The breakdown by type of product is in the analysis of the impact of management fees on long-term returns.

The formula also assumes that gains stay invested. A yearly levy on interest lowers the rate of every period, whereas a levy at exit applies only once. With a hypothetical 30% tax rate, €10,000 invested at 5% for 30 years gives €28,068 if the tax is paid every year (the net rate falls to 3.5%), and €33,254 if it is paid once on the final gain. At an equal tax rate, the annual levy cuts the final capital by 16%. A partial withdrawal shrinks the base instead: the amount withdrawn stops earning interest for all the remaining years.

What the calculation doesn’t show: inflation, fees, behavior

The theoretical calculation assumes a constant rate and regular compounding. Several factors pull the real outcome away from the headline figure. The simulator above shows inflation, fees and the behavior gap; taxes stay outside the tool.

Inflation erodes the purchasing power of accumulated capital. A 5% nominal return with 2% inflation produces a real return of about 3%. It is the difference between the figure on the statement and what it can actually buy, the distinction between nominal and real returns. To isolate that effect, the dedicated real return after inflation calculator computes it directly.

Taxes and fees reduce the effective return through the same exponent as the gains (see the trade-off between duration, rate and fees). The tax treatment of gains differs by wrapper, as the comparison of a PEA and a taxable brokerage account shows, and can materially affect the net amount.

The behavior gap. The return actually captured by the average investor can be lower than the return of the instruments held, largely because entry and exit decisions are poorly timed. The simulator’s “Include the average behavior gap” box takes 1.5 points off the return, an assumption drawn from the Dalbar QAIB methodology and contested, since other studies find a smaller gap. At the default setting, the “After behavior gap” card then shows €223,685, and the “Real purchasing power” card, which deflates that lower projection, falls to €123,490.

Frequently asked questions

How do you calculate compound interest?

The formula is A = P × (1 + r/n)^n×t, where P is the principal, r the annual rate, n the number of compounding periods per year and t the duration. With annual compounding it simplifies to A = P × (1 + r)^t. The simulator above performs this calculation automatically and adds the effect of inflation.

How do you calculate compound interest with monthly contributions?

The future value of the contributions is added to the compounded starting capital: FV = C × ((1 + i)^N − 1) / i, with i the monthly rate and N the number of months. €100 paid in every month for 20 years at 4%, compounded monthly, gives €36,677 for €24,000 paid in.

Monthly or annual compounding: how big is the difference?

At an equal stated annual rate, monthly compounding produces slightly more, because each month’s interest starts earning interest the following month. Over 30 years at 7%, €10,000 becomes €81,165 with monthly compounding against €76,123 with annual compounding. The gap grows with duration and rate.

What’s the difference between simple and compound interest?

Simple interest is computed on the principal only (linear growth); compound interest folds prior interest into the base (exponential growth). Over 30 years, €10,000 at 5% gives €25,000 with simple interest against €43,219 with compound interest. The same arithmetic underlies the SEC’s compound interest calculator on Investor.gov.

How long does it take to double your money?

The rule of 72 gives a quick estimate: 72 ÷ annual rate. At 5%, capital doubles in about 14.4 years; at 3%, in about 24 years. The approximation holds well for rates between 2% and 15%.

Does the simulator account for inflation?

Yes. The “real purchasing power” curve deflates the nominal projection (the after-gap projection when the behavior gap box is ticked) by the average inflation entered, in today’s euros. At 2% inflation, capital loses close to half its purchasing power over 30 years. The mechanism is detailed in the real return on savings after inflation.

What return does the simulator assume?

By default, 7% a year: a calculation setting, not an estimate. The simulator computes what the assumptions entered produce, without judging them. The rate on a regulated savings account such as France’s Livret A is set by the authorities and in principle reviewed twice a year. For risky assets, the average historical return depends heavily on the period chosen and says nothing about future returns. A constant rate does not reproduce volatility or the order of good and bad years either.

Key takeaways

• Compound interest creates exponential growth: interest itself earns interest.
• Duration is the most powerful lever: most of the gains concentrate in the later years.
• 30 years at 4% give about as much as 20 years at 6%, and fees, like a yearly tax, go through the same exponent.
• Inflation, fees, taxes and the behavior gap separate the nominal figure from purchasing power.
• A calculator makes visible the assumptions under which the outcome holds, without predicting that outcome.

Last updated — 21 October 2026