Free Online Compound Interest Calculator

What the compound interest calculator shows

This compound interest calculator estimates how money can grow when returns are reinvested and earn returns of their own. You enter a starting amount, an optional monthly contribution, an expected annual return, a time horizon and a compounding frequency. The calculator then shows what the balance could be worth at the end, how much of it is money you put in, and how much is growth.

Compound interest is simple to describe and hard to feel intuitively. In the first years the growth looks small. Later, the growth earned on earlier growth starts to dominate the result. The chart and the year-by-year table make that shift visible, which is often more useful than the final number itself.

The calculator is built for planning questions such as: how much could a lump sum become in 20 years, how much does a regular monthly contribution add, what changes if I contribute for only part of the period, and how sensitive is the result to the return I assume. It runs entirely in your browser, and nothing you type is sent anywhere.

In this guide:

• How to fill in every field and read the results
• The exact compound interest formula the calculator uses, and its assumptions
• Simple vs compound interest, compounding frequency and the rule of 72
• Reference tables and three worked examples in US dollars
• Common mistakes and what the calculator cannot tell you

If you are new to the idea, the basics article on compound interest and the time value of money explains the concept step by step before you start experimenting with numbers.

How to use the compound interest calculator

The inputs appear in the order below. The calculator opens in US dollars with the default values in the table below, and the examples in this guide keep USD. On wide screens the UAH / USD / EUR switch sits in the header of the Your numbers panel; on phones and tablets it is under More options. The currency changes only how numbers are shown, not the math.

Each of the four main inputs has a number box and a slider. Type a value to go beyond the slider's range.

1. Initial amount. The money you invest at the start. Enter 0 if you start from nothing. The slider runs to 100,000 in USD or EUR and to 2,000,000 in UAH.
2. Monthly contribution. The amount you add every month. Enter 0 to model a single lump sum. The slider runs to 5,000 in USD or EUR and to 100,000 in UAH.
3. Expected annual return. The nominal yearly rate you assume, in percent. The slider covers 0% to 15%, and you can type up to 50%. The Conservative, Moderate and Aggressive chips under the slider set 5%, 8% or 11% in one click.
4. Investment period. The total number of years the money stays invested, from 1 to 50.

More options is collapsed at first and holds the rest:

• Compounding frequency. Monthly, Quarterly, Semiannual or Annual.
• Months with contributions. How many months, counted from the start, you keep adding the monthly contribution.
• A note that monthly contributions are added at the end of each month.

On phones, the two money fields use − and + buttons instead of a slider, in steps of 1,000 and 50 in USD or EUR. The return and the period keep their sliders.

Months with contributions follows the investment period while the two match. If you change the period and contributions currently cover the whole horizon, they keep covering it. If you have set a shorter contribution window, it stays as it is, and is only cut back if the new period is shorter than the window.

Reading the results

On wide screens the results sit to the right of the inputs and stay in view while you scroll. The headline, Final portfolio value after N years, is the balance at the end of the period. A bar under it splits that balance in two, with a figure for each part. You put in is everything you contributed, and it includes the initial amount as well as every monthly contribution. Growth is the difference between the two, with its share of the final balance in brackets.

Below that, two tabs show the path to the result. Chart stacks your contributions and the growth for each year, with the portfolio line on top. Year by year lists, for every year, the cumulative contributions, the cumulative growth and the end balance. Watch the year in which the growth column overtakes the contributions column: that is where compounding starts doing more of the work than your saving.

Four buttons sit next to the headline:

• Pin to compare keeps the current inputs as a reference while you try others. The headline then shows the difference, such as +$25,000 vs pinned, the chart adds the pinned balance as a dashed line, and a Pinned scenario caption lists the pinned inputs. The pin lives only in memory: switching the currency, Reset or reloading the page clears it.
• PDF exports the inputs, the summary (final portfolio value, total contributions and total investment gain) and the yearly table. The pinned scenario is never included.
• Share shares a link to the page, without your numbers.
• Reset, the round-arrow button on wide screens, restores the defaults.

On phones and tablets, the results live in a bar fixed to the bottom of the screen. It always shows the headline and updates as you change the inputs. Details opens the figures, the two tabs and the buttons, and Less closes them again.

How the compound interest formula works in this calculator

The classic compound interest formula

For a single amount with no contributions, the textbook compound interest formula is:

A = P × (1 + r/n)^(n × t)

• A is the amount after t years
• P is the principal, the starting amount
• r is the nominal annual rate as a decimal (8% is 0.08)
• n is the number of compounding periods per year (12 monthly, 4 quarterly, 2 semiannual, 1 annual)
• t is the number of years

The rate is divided by n because the nominal rate is quoted per year but applied per period. The exponent counts how many times interest is added in total.

From the annual rate to a monthly rate

The calculator steps through time one month at a time, because contributions are monthly. It therefore converts the nominal rate and the compounding frequency you choose into one equivalent monthly rate:

i = (1 + r/n)^(n/12) − 1

With monthly compounding this is simply r/12: at 8% the monthly rate is 0.6667%. With annual compounding the same 8% becomes 0.6434% per month, which, compounded over 12 months, gives exactly 8% for the year. Because the conversion is exact, a lump sum shows the same yearly values as the classic formula for every frequency. With 8% and annual compounding, $10,000 becomes $21,589 after 10 years either way.

How monthly contributions are added

Each month the calculator does two things, in this order:

balance = balance × (1 + i)
balance = balance + PMT     (while month ≤ c)

PMT is the monthly contribution and c is the number of months with contributions. Because growth is applied before the contribution, each contribution is added at the end of its month and starts earning from the next month. When contributions run for the whole period of m months, the loop gives the same result as the closed-form future value:

FV = P × (1 + i)^m + PMT × ((1 + i)^m − 1) / i

When contributions stop after c months, the balance at that point keeps compounding for the remaining m − c months with nothing added.

Assumptions behind the numbers

• Constant return. The same rate applies every month. Real returns vary, sometimes sharply, and can be negative for years.
• End-of-month contributions. Contributions are added after the month's growth. Investing at the start of each month would give a slightly higher result.
• Contributions start in month one and run for the number of months you set. A contribution gap in the middle cannot be modelled.
• Fixed contribution. The monthly amount does not rise with pay or inflation.
• Compounding frequency sets the effective rate. Growth is applied monthly at the equivalent rate even when you choose annual compounding, so money added mid-year earns a proportional share of that year's growth. A bank that credits interest only once a year may treat deposits made during the year differently.
• Not modelled: taxes, fees, inflation, currency conversion and withdrawals. All results are nominal and before costs.

Simple vs compound interest

The difference between simple and compound interest is what the interest is calculated on. Simple interest is always paid on the original principal only. Compound interest is paid on the principal plus the interest already earned. That is the whole answer to "what is compound interest in math": a growth rate applied to a balance that includes past growth, which turns a straight line into a curve.

With simple interest, $10,000 at 6% earns $600 every year, forever. With compound interest, the first year also earns $600, but the second year earns 6% of $10,600, and so on. The gap is invisible at first and then widens quickly:

The table assumes $10,000 at 6% per year, no contributions and annual compounding for the compound column. The simple-interest column uses P × (1 + r × t), which this calculator does not model, because almost every savings or investment product that reinvests its income compounds.

Two practical points follow. First, compounding only happens when returns stay invested. If interest or dividends are paid out and spent, the growth behaves like simple interest. Second, the table shows why the early years can feel disappointing: after five years the compounding bonus is less than 4% of the starting amount. Time is the ingredient that makes the difference large, which is the main theme of the time value of money.

Compounding frequency and the compounding period

The compounding period is how often earned interest is added to the balance so that it starts earning interest itself. Savings products usually state a nominal annual rate together with a compounding frequency. The more often interest is added, the higher the effective annual rate for the same nominal rate.

The effective annual rate (sometimes called the annual percentage yield) is:

EAR = (1 + r/n)^n − 1

Here is the same $10,000 at 8% nominal per year with no contributions, using each frequency the calculator offers:

Monthly compounding beats annual by $607 after 10 years and by $8,730 after 30 years. That is real money, but it is small next to changes in the rate or the horizon. Adding $500 a month for 30 years at 8% gives $745,180 with monthly compounding and $704,275 with annual compounding. Changing the rate by one percentage point moves the result much more: with monthly compounding the same plan gives $609,985 at 7% and $915,372 at 9%.

Compounding frequency matters most when you compare two products that quote the same nominal rate in different ways. In that case, compare effective annual rates, not headline rates. For investments such as stock funds there is no contractual compounding schedule at all: the growth comes from price changes and reinvested dividends. For those, treat the expected annual return as an effective yearly rate and choose Annual compounding, so the calculator does not add the small extra from more frequent compounding to an assumption that already includes it.

The calculator does not offer daily compounding. At typical rates the effective annual rate of daily compounding is only marginally above monthly compounding, so the monthly setting is a close approximation.

The rule of 72

The rule of 72 is a mental shortcut for doubling time: divide 72 by the annual rate in percent, and the result is roughly how many years it takes money to double. At 8%, 72 ÷ 8 = 9 years. The calculator confirms it: $10,000 at 8% with annual compounding reaches $19,990 after 9 years and $21,589 after 10.

The exact doubling time for annual compounding is:

years to double = ln(2) ÷ ln(1 + r)

The rule works because ln(2) is about 0.693, and for moderate rates ln(1 + r) is a little less than r, so dividing 72 by the rate in percent lands close to the true answer. It is most accurate around 8%:

The rule also works in reverse. If you want to double your money in 10 years, you need roughly 7.2% a year (7.18% exactly with annual compounding). And it works for anything that compounds, including costs: at 3% inflation, prices double in about 24 years by the rule (23.4 years exactly), which means the purchasing power of cash held at a zero interest rate halves over the same period. The inflation basics article explains why that matters for long-term goals.

Time, rate and monthly contributions

Three levers drive a compound interest result: how long the money is invested, the return it earns, and how much you add. The calculator lets you move each one separately, and the effects are not equal.

Time and rate together

A common question is how much a sum will be worth in 20 years. Here is $50,000 with no further contributions and monthly compounding, at the three quick return scenarios:

Read down a column and you see the effect of time; read across a row and you see the effect of the rate. Both interact: the gap between 5% and 11% is $67,107 after 10 years and over $1.1 million after 30. Higher assumed returns usually come with more risk, meaning a wider range of possible outcomes and deeper temporary losses. The risk and return article explains that trade-off, and why an 11% assumption is not simply a better plan than a 5% one.

Lump sum versus monthly contributions

Suppose you will invest $60,000 over 10 years at 7% with monthly compounding. If you invest it all on day one, the calculator shows $120,580. If you invest $500 a month for 120 months instead, the result is $86,542. Splitting it, $30,000 up front plus $250 a month, gives $103,561. The total contributed is $60,000 in all three cases.

The lump sum wins in this model because every dollar is invested for the full period. In practice most people do not have the full amount on day one, and investing monthly from income is the realistic option. Spreading purchases over time also reduces the risk of investing everything just before a market fall, which this constant-return model cannot show. The dollar-cost averaging article covers that side, and the dollar-cost averaging calculator models it with your numbers.

The downside of compound interest

Compounding is neutral: it amplifies whatever rate it is given. That has three consequences that the headline numbers can hide.

Debt compounds too. A $5,000 balance at 24% a year, compounded monthly, with no payments, grows to $6,341 after one year, $10,199 after three and $16,405 after five, using this calculator's math. Real credit-card statements differ in detail, but the direction is the same. Paying off high-interest debt works like a guaranteed return equal to the interest rate you stop paying, which few investments can match. The loan and mortgage calculator shows how interest builds up on a repayment schedule.

Costs and inflation compound against you. A fund fee of 1% a year sounds small, but it is taken from a growing balance every year. Inflation reduces what each future dollar buys. The calculator shows nominal values before both, but you can approximate them by lowering the return. Here is $10,000 plus $300 a month for 30 years with monthly compounding:

Total contributions are $118,000 in every row. The 3.9% figure is the real return implied by 7% nominal growth and an assumed 3% inflation, (1.07 ÷ 1.03) − 1 = 3.88%, rounded to one decimal place for the table (the rate field also accepts 3.88 if you prefer the exact figure); the last row does the same for 6% after fees, (1.06 ÷ 1.03) − 1 = 2.91%. Subtracting a fee from the return is an approximation; the fees drag calculator models costs directly, and the inflation impact calculator shows the purchasing-power side.

Compounding needs time, and returns are not smooth. In the early years most of the balance is your own money, so a bad year in the market is felt in full while the compounding bonus is still small. The steady curve in the chart is a model; a real portfolio gets there, if it does, along a bumpy path.

Compound growth at a glance

These two tables give quick reference values computed with the calculator's own math, with monthly compounding and no taxes, fees or inflation. Because the math is proportional, you can scale them: double the amount and the result doubles.

$10,000 invested once, no contributions:

$100 a month, added at the end of each month, starting from zero:

The contributions alone are $12,000 after 10 years, $24,000 after 20, $36,000 after 30 and $48,000 after 40. Everything above those figures is growth. To combine a lump sum with monthly saving, add the two results: $10,000 plus $100 a month for 20 years at 6% is $33,102 + $46,204 = $79,306.

Worked examples

Each example below uses USD as the display currency and shows exactly what the calculator returns for the inputs listed.

Common mistakes when estimating compound growth

• Treating the expected return as a promise. The calculator applies one steady rate. Markets do not, so use several rates and plan for the lower ones.
• Double counting compounding for market returns. Long-run stock or fund returns are usually quoted as annualised (compound annual) rates, which already include compounding. Choosing Monthly compounding on top adds a small extra that the original figure does not contain; Annual is the closer match.
• Forgetting that the initial amount is a contribution. Total contributions include the starting balance, so the gain figure is growth only, not growth plus your first deposit.
• Ignoring fees, taxes and inflation. All results are nominal and before costs. A real return a few points lower changes long-term results a lot, as the downside table shows.
• Comparing products by nominal rate alone. Two savings products with the same headline rate can pay different amounts if they compound differently. Compare effective annual rates.
• Assuming contributions start at the beginning of the month. The calculator adds them at the end, so if your own platform invests on the first day, your real result would be slightly higher.
• Setting the period and forgetting the contribution window. If you shortened Months with contributions earlier, extending the period keeps that shorter window. The field sits under More options, so check it there after each change.
• Using a single rate for very long horizons. A rate that seems reasonable for 10 years is a much bigger assumption over 40, because errors compound as well.

Limitations and next steps

This calculator answers one question well: how a balance grows at a constant rate with regular contributions. It does not know your taxes, the fees you pay, the inflation you will face, the order in which good and bad years will arrive, or whether you will need the money early. It cannot tell you which investments to choose or what return they will earn.

Use it to understand the shape of compound growth and to compare scenarios side by side, then test the parts it leaves out:

• The investment goal calculator works backwards from a target amount to the monthly contribution needed.
• The fees drag calculator shows how much annual costs take from the final balance.
• The inflation impact calculator turns future amounts into today's purchasing power.

For background, read what investing is and how different types of investment assets carry different levels of risk. For decisions about your own savings, taxes or retirement, consider a qualified, independent financial adviser who can take your full situation into account.