Compound Interest Calculator
Future value: $0
What would you like to solve for?
Project a balance, or work backwards from a goal to the input you need.
Enter an initial amount or a regular contribution to project growth.
Advanced: fees, tax & inflation
- Contributions$0
- Interest$0
Return metrics
Investment growth
How your money grows, step by step
Each row builds on the one above it, from your first deposit to the inflation-adjusted balance you can actually spend.
- Initial investment+ $0
- Regular contributions added+ $0
- Total money invested$0
- Compound interest earned+ $0
- Balance$0
- Value in today's money$0
Compound vs simple interest
Simple interest is paid only on the money you put in. Compound interest also earns interest on past interest — the gap widens every year.
- With compounding$0
- Simple interest only$0
The compounding advantage grows over time
Accumulation schedule
| Year | Contribution | Interest | Balance |
|---|
Contribution and interest are the amounts added during each period; balance is the running total at the end of it.
The compound interest formula
A one-off deposit grows by the compound interest formula. This tool steps month by month so it can also fold in your contributions, fees, tax and inflation.
A = P · (1 + r/n)^(n·t)where:
- A
- the final balance
- P
- the initial principal you start with
- r
- the annual interest rate as a decimal (7% = 0.07)
- n
- how many times interest compounds per year
- t
- the number of years invested
A = P · e^(r·t)Each regular contribution is added on its schedule and then compounds for the time it has left invested — the future value of an annuity.
An annual management fee is charged on the balance as it grows, so it quietly lowers the effective return.
Tax is applied to your total gain at the end (as on withdrawal), so it never changes how the balance compounds along the way.
Inflation never alters the nominal balance — it only restates the result in today's purchasing power.
Worked example
Invest 10,000 at a 7% annual rate compounded monthly for 25 years with no contributions. Here n = 12 and t = 25, so A = 10,000 × (1 + 0.07/12)^(12 × 25) ≈ 57,254 — the balance grows more than fivefold, and about 47,254 of it is interest your money earned on its own.
With your numbers
A $0 start at 0% compounded monthly for 0 years grows to $0 — $0 of it interest.
Input definitions
- Initial investment
- The lump sum you begin with, before any contributions or interest.
- Regular contribution
- An amount you add on a fixed schedule — monthly, quarterly, semi-annually or annually.
- Annual interest rate
- The nominal yearly rate of return, before compounding is applied.
- Compounding frequency
- How often interest is added back to the balance. More often means faster growth; continuous is the theoretical limit.
- Management fee
- An annual percentage charged on your balance, such as a fund's expense ratio — it lowers your effective return.
- Tax on gains
- The rate applied to your total investment gain when you withdraw, reducing your after-tax value.
- Inflation rate
- The assumed annual rise in prices, used to show your balance in today's purchasing power.
Know what this estimate is based on
- Jurisdiction
- No statute sets these results — they are return, fee and time-value arithmetic that holds in any market. Tools in this category that do turn on U.S. tax law or a contribution limit say so on their own page.
- Scope and limitations
- Scenario model, not a forecast. Returns, volatility, inflation, fees and taxes are assumptions you supply, and actual investment outcomes can be lower or negative. Past performance does not carry forward, and no allocation shown here is a recommendation.
- Source links checked
- Sep 19, 2026
Built and regression-tested by Smart Tools Lab. It has not been individually reviewed by a licensed financial, tax, or legal professional.
How to use
- 01
Choose what to solve for: the future value of your plan, or work backwards from a goal balance to the required contribution, starting amount, return rate, or time needed.
- 02
Enter your initial investment and a regular contribution, set how often you add it (monthly, quarterly, semi-annual or annual), then set the annual interest rate, the duration and how often interest compounds — from annually all the way to continuous.
- 03
Open Advanced for an annual management fee, tax on gains and an inflation rate, then read the future value, the return metrics (EAR, CAGR, annualized return and the Rule of 72), the growth and comparison charts, the step-by-step breakdown and the year-by-year and month-by-month schedule.
- 04
Save scenarios to compare different rates, contributions or durations side by side, or copy a share link that reopens the exact projection.
Formula
For a principal with no contributions, A = P × (1 + r ÷ n)ⁿᵗ, where P is principal, r is the nominal annual rate, n is compounds per year and t is years. For equal end-of-period deposits at the same periodic rate i, add PMT × ((1 + i)ᴺ − 1) ÷ i. Beginning-of-period deposits multiply that annuity term by (1 + i). The calculator month-steps the general case so contribution and compounding frequencies can differ.
Example
Invest $10,000 for 5 years at a 6% nominal rate compounded monthly, with no further deposits, fees or tax. The result is $10,000 × (1 + 0.06 ÷ 12)⁶⁰ = $13,488.50, so compound interest contributes $3,488.50.
Definitions
- Principal
- The amount invested before any interest or later contributions.
- Nominal rate
- The quoted annual rate before the effect of within-year compounding.
- Compounding frequency
- How often earned interest is added to the balance and begins earning interest itself.
- Contribution timing
- Whether each recurring deposit arrives at the beginning or end of its contribution period.
- Effective annual rate
- The actual one-year growth rate after compounding the nominal rate.
Good to know
What compound interest really is
Compound interest is interest that earns interest. Most people first meet its plainer cousin, simple interest, where a deposit earns the same flat amount every year and nothing more. Compounding is different: each period's gain is added to your balance, and the next period's interest is calculated on that larger total, so your returns start generating returns of their own. The balance grows not in a straight line but along an accelerating curve, and the longer it runs the steeper that curve becomes. Albert Einstein is often — probably apocryphally — quoted calling it the eighth wonder of the world, adding that those who understand it earn it and those who don't pay it. The arithmetic behind that reputation is striking. Consider a plain example: you start with $10,000, add $500 a month, and earn 7% a year compounded monthly for 25 years. You will have put in just $160,000 of your own money (the $10,000 start plus $500 × 12 × 25 in deposits), yet the account finishes at about $462,290. The extra $302,290 — nearly two-thirds of the final balance — is pure compound growth, money your money earned without any further effort from you. The single most important lesson is that the effect is heavily back-loaded: it feels disappointingly slow in the early years, when there is little accumulated interest to compound, and then becomes dramatic late on, when each year's gain is computed on a balance that has grown many times over. That asymmetry is exactly why patience and an early start matter more than almost any other decision a saver makes, and why the same mechanism, pointed at debt, can quietly destroy wealth just as fast as it builds it.
How this calculator models growth
A one-off deposit follows the textbook compound interest formula A = P(1 + r/n)^(n·t), where P is the principal, r the annual rate written as a decimal, n how many times interest compounds per year, and t the number of years. For continuous compounding — the theoretical limit of ever-more-frequent compounding — the formula becomes A = P·e^(r·t). Those equations describe a single untouched lump sum, but real plans involve regular deposits, fees, tax and inflation, so this tool does not just plug numbers into a formula. Instead it steps forward month by month. Each month it multiplies the running balance by the effective monthly growth factor for your chosen compounding frequency, adds any contribution that falls due that month at the beginning or end of the period, and deducts a slice of the annual management fee. Because every contribution is added on its own schedule and then compounds only for the time it has left invested, the result is the future value of an annuity stacked on top of the growing lump sum. Stepping monthly keeps the math exact at every year boundary for any compounding frequency, while producing the clean month-by-month and year-by-year schedules you can scroll through below the results, and the inflation, tax and fee adjustments are layered on top without ever distorting the underlying compounding path. This is also why the calculator can run in reverse: because the future value is a predictable function of each input, it can solve backwards for the contribution, starting amount, rate or time you would need to hit a goal. Treat the projection as a disciplined model of a steady assumed rate, not a forecast of what volatile markets will actually deliver in any single year.
Simple versus compound interest
The gap between simple and compound interest is the whole story of long-term investing, and the comparison chart in this tool is built to make it visible. Under simple interest, only the money you put in ever earns a return; past interest sits idle and never works for you. Under compounding, that past interest is reinvested and earns alongside your principal, so the engine that drives your balance keeps getting bigger. On a $10,000 start with $500-a-month deposits at 7%, simple interest would reach only about $308,000 over 25 years, while compounding reaches $462,290 — a difference of roughly $154,000 earned purely because interest was allowed to earn interest. Early on the two paths are almost indistinguishable, because there is little accumulated interest to compound and the curves overlap. But the gap widens every single year, slowly at first and then rapidly, and over a long horizon it becomes enormous; most of that $154,000 advantage is created in the final decade. This is why high-interest debt is so dangerous and long-term saving so powerful: they are the same mechanism pointed in opposite directions. A credit-card balance compounds against you exactly as an investment compounds for you, which is why paying down compounding debt often beats investing as the highest-certainty return available. The practical lesson is to get on the compounding side of the equation as early and as fully as you can — clear the debts that compound against you, then let time turn a modest, steady savings habit into a balance that dwarfs what you actually contributed.
Why compounding frequency matters (a little)
Compounding frequency is how often interest is calculated and added back to your balance — annually, semi-annually, quarterly, monthly, weekly, daily, or continuously. More frequent compounding means interest starts earning interest sooner, so it nudges your return upward, but the effect is smaller than most people expect at ordinary rates. The honest measure is the effective annual rate (EAR), which folds compounding into a single comparable number: EAR = (1 + r/n)^n − 1, or e^r − 1 when continuous. A 7% nominal rate works out to an effective 7.00% compounded annually, about 7.23% compounded monthly, and about 7.25% compounded daily or continuously. So moving all the way from annual to daily compounding adds only around a quarter of a percentage point. On a $10,000 lump sum left for 25 years that is the difference between roughly $54,300 with annual compounding and about $57,500 with continuous — a real gain of a little over $3,000, but a far cry from the headline balance. The reason it matters at all is comparison: two accounts can quote the same nominal rate yet pay differently because one compounds monthly and the other annually, and EAR is the only fair way to line them up. Frequency matters more the higher the rate and the longer the horizon, so it is worth checking on a large, long-term holding. But do not let a marginally more frequent compounding schedule distract you from the inputs that move the needle far more — the rate itself, the size of your contributions, and above all the number of years you stay invested.
Contributions, timing, and the power of starting early
For most savers, regular contributions do more heavy lifting than the headline rate, because they feed the snowball more snow to roll. This calculator lets you contribute monthly, quarterly, semi-annually or annually, and because money added sooner compounds for longer, more frequent contributions of the same yearly total finish slightly ahead — twelve $500 deposits beat a single $6,000 deposit made at year end. The contribution-timing switch makes a smaller but real difference of its own: deposits made at the beginning of each period earn one extra period of growth compared with end-of-period deposits, so choosing 'beginning' always produces a marginally higher balance, an edge that itself compounds over decades. The biggest lever of all, though, is time. Because compounding is back-loaded, a saver who starts ten years earlier often ends up far ahead of someone who contributes more but starts late, since the early money has the most years to compound and those final, fastest-growing years are the ones the late starter misses entirely. A dollar invested at 25 has forty years to work; the same dollar invested at 45 has only twenty, and at 7% that difference is the gap between roughly fifteen-fold and four-fold growth. The practical takeaways are simple and well supported by the math: start as early as you can, even with small amounts; automate your contributions so they happen without a monthly decision; and raise them whenever your income rises, since each increase is magnified dramatically over the years that follow. Consistency, not perfect timing or a perfect rate, is what compounding rewards.
Working backwards from a goal
Projecting a future value is only half of financial planning; just as often you know the target and need to find the input that reaches it. This calculator's five modes let you solve in either direction. 'Future value' projects forward from your inputs. The other four work backwards from a goal balance: 'Required contribution' finds the regular deposit needed, 'Required initial amount' the lump sum, 'Required return rate' the annual return your plan demands, and 'Time needed' the number of years. The numbers make this concrete. Reaching $1 million in 25 years from a $10,000 start at 7% calls for about $1,164 a month — a useful reality check on whether a goal fits your budget. Asking instead what return you would need to reach $600,000 from that $10,000 start with $500 a month, the calculator solves for about 8.5% a year, which tells you immediately whether the goal demands more risk than you are comfortable taking. Each reverse mode reaches exactly the same projection from the opposite direction, and crucially each one tells you when a goal is genuinely out of reach — when even a 100%-a-year return or a full century of saving would not get there — instead of quietly displaying an impossible figure dressed up as a plan. This is where a compounding tool becomes a planning instrument rather than a curiosity: you can test a retirement number against your real contribution capacity, discover the rate a goal implicitly requires, or find out how many more years of patience would close the gap. Treat an implausibly high required rate as a signal to lower the goal, lengthen the horizon, or save more, not as a target to chase with reckless risk.
Fees: the silent compounding drag
An annual management fee — a fund's expense ratio, an advisor's percentage, a platform charge — looks trivial as a single number and is anything but over a lifetime, because it is levied every year on a growing balance and quietly removes money that would otherwise have compounded for you. The tool models this as a drag on the balance as it grows, and the fee-impact chart shows the damage in stark terms. On that $10,000-plus-$500-a-month plan, a 1% annual fee cuts the final balance from $462,290 to about $390,473 — roughly $71,800 less. Strikingly, only about $38,900 of that loss is fees you actually handed over; the remaining $33,000 or so is the growth those fees never got the chance to earn, the compounding you forfeited by having a smaller balance every year. That is the true and counterintuitive cost of fees: not the percentage skimmed in any one year, but the lifetime of compounding you give up. It is the single strongest argument for low-cost index funds over expensive actively managed ones, because over decades a one- or two-percent annual fee difference can swallow a quarter or more of your gains while delivering nothing extra in return. The damage scales with both time and balance, so it hits long-term retirement money hardest of all. When you compare any two investments, compare them net of fees rather than on headline returns, treat a high expense ratio as the persistent headwind it really is, and remember that a fee saved compounds in your favor exactly as a fee paid compounds against you. Cutting a 1% fee to 0.1% is, over a long horizon, one of the most reliable returns available to any investor.
Taxes and inflation: what you actually keep
A projected balance is a gross, nominal figure; what you can actually spend is smaller, and two forces explain the gap. The first is tax. This calculator applies tax to your total gain at the end, the way a capital-gains tax works when you sell or withdraw, which keeps the balance compounding untouched along the way and is generally the most favorable common treatment. On a $10,000 start with $500 a month at 7% for 25 years, a 15% rate turns the $462,290 balance into about $416,947 after roughly $45,344 of tax on the $302,290 of gains. An account taxed every year instead — as interest in a regular savings account often is — would end a little lower, because tax paid early can no longer compound, which is precisely why tax-advantaged retirement accounts are so valuable: they let the full, pre-tax balance keep working for years or decades longer. The second force is inflation, which never changes your nominal balance but steadily erodes what it can buy. Adjusting the same plan for 2.5% annual inflation, the $462,290 is worth only about $249,355 in today's money — a sobering reminder that a big future number is not the same as a big future lifestyle, and that a 'safe' return below the inflation rate is really a slow loss in disguise. The lesson is to judge a plan by its real, after-tax outcome rather than its headline figure: favor tax-advantaged accounts wherever you can, hold long enough to benefit from lower long-term capital-gains treatment where it applies, and make sure your assumed return comfortably clears inflation with room to spare. The 'value in today's money' line and the after-tax figure exist precisely so you can see the spendable result, not just the impressive-looking gross total.
Reading the return metrics: CAGR, annualized return and the Rule of 72
The results panel reports several rates, and they are not interchangeable — confusing them is one of the most common ways people misread a projection. The effective annual rate (EAR) describes the account's terms: your nominal rate once compounding is included. CAGR, the compound annual growth rate, is the single steady rate that would turn your total money in into the final balance if every dollar had been invested on day one; on a $10,000 start with $500 a month at 7% for 25 years that is only about 4.34%, which looks surprisingly low precisely because most of the $160,000 was added gradually over 25 years rather than sitting there from the start. The annualized (money-weighted) return fixes that distortion by accounting for when each contribution actually arrived, giving about 7.23% for that plan — far closer to the return you genuinely earned on the money while it was invested, and the fairer measure for any steady savings plan. In short, CAGR understates the return of a drip-fed account, while the annualized figure reflects it honestly; for a single lump sum the two coincide. The Rule of 72 is the quick mental shortcut that ties it all together: divide 72 by the annual rate to estimate the years it takes money to double, so 7% doubles in roughly 10.3 years, 6% in about 12, and 10% in a little over 7. It is an approximation, most accurate for rates between about 6% and 10%, but it is a wonderful way to sense-check a plan in your head before you ever open a calculator — if a 'doubling in five years' claim implies a 14%-plus return, you know to be skeptical. Read these metrics together rather than fixating on any single one.
Strategies, real-world examples and common mistakes
Put the principles together and a clear playbook emerges. Start early, because time is the most powerful and least replaceable input you have. Automate contributions so consistency does not depend on willpower or memory, and raise them whenever your income does. Keep costs low, since fees compound against you just as returns compound for you. Use tax-advantaged accounts wherever they exist, reinvest dividends and interest so they can compound rather than leak away, and always judge outcomes in real, after-tax terms. A few worked numbers make the stakes concrete: at a 7% return a single $10,000 deposit grows to about $57,254 over 25 years untouched, more than fivefold; adding $500 a month turns it into $462,290; and the same plan exposed to a 1% fee, a 15% tax, or 2.5% inflation lands meaningfully lower at every stage, which is exactly why the advanced options reward exploring rather than ignoring. The common mistakes are the mirror image of the playbook, and they are remarkably consistent across investors. People expect growth to look linear and give up during the slow early years, just before the curve would have steepened. They wave away fees because 1% sounds small, not realizing it can cost tens of thousands. They quote a gross return and forget tax and inflation, mistaking a nominal number for spendable wealth. They chase a marginally higher compounding frequency instead of a higher rate, more savings, or more time. And they assume a single steady rate when real markets are volatile, then panic when a bad year arrives. Treat every projection here as a disciplined planning guide and a realistic range, not a promise — diversify, give your money time, keep your costs and taxes low, and let the mathematics of patience do the heavy lifting. The future is uncertain, but the direction compounding points a consistent saver is not.
Frequently asked questions
How does this calculator work out the future value?
It steps month by month rather than plugging numbers into the one-line formula. Each month it grows the balance by the effective monthly factor for your chosen compounding frequency, adds any contribution due that month at the start or end of the period, and deducts a share of the annual fee. That lets it handle contributions, fees, tax and inflation together — things the textbook A = P(1 + r/n)^(n·t) formula can't, since that describes only a single untouched deposit.
What do the five 'solve for' modes do?
Future value projects forward from your inputs. The other four work backwards from a goal balance: 'Required contribution' finds the regular deposit needed, 'Required initial amount' the lump sum, 'Required return rate' the annual rate, and 'Time needed' the number of years. If a goal can't be reached with a realistic return or within 100 years, the calculator says so rather than showing an impossible figure.
Is tax applied as interest is earned or at the end?
At the end, on your total gain, the way a capital-gains tax applies when you sell or withdraw. This keeps the nominal balance compounding untouched along the way and shows the after-tax value separately. On a $10,000 start with $500 a month at 7% for 25 years, adding a 15% tax rate turns the $462,290 balance into about $416,947 after roughly $45,344 of tax on the gains. If your account is taxed each year instead, your real outcome will be a little lower than this withdrawal-style estimate.
Why are CAGR and the annualized return different?
They answer different questions. CAGR is the rate that would turn your total money in into the final balance if it had all been invested on day one — on a $10,000 start with $500 a month for 25 years that is about 4.34%, low because most of the $160,000 was added gradually, not up front. The annualized (money-weighted) return accounts for when each contribution actually went in, giving about 7.23% — much closer to the rate you earned. For a steady savings plan the annualized figure is the fairer measure.
Does compounding frequency really change much?
Less than most people expect at normal rates. A 7% nominal rate is an effective 7.00% compounded annually, 7.23% compounded monthly, and 7.25% compounded daily or continuously — so moving from annual to daily compounding adds about a quarter of a percentage point. Over a 25-year lump sum that is the difference between roughly $54,300 and $57,500 on a $10,000 deposit. It matters more the higher the rate and the longer the horizon.
How badly do fees hurt long-term growth?
Far more than the headline percentage suggests, because the fee is charged every year on a growing balance and quietly removes money that would otherwise have compounded. On a $10,000 start with $500 a month at 7% for 25 years, a 1% annual fee cuts the final balance from $462,290 to about $390,473 — roughly $71,800 less. Only about $38,900 of that is fees actually paid; the rest is the growth those fees never got to earn. The fee-impact chart makes this drag visible.