How compound interest works
Compound interest is the interest you earn on your interest. In the first year, you earn a return on the money you put in. In the second year, you earn a return on your original money plus the gains from year one — and on and on. That small loop, repeated for years, is what turns steady saving into a much larger number than you'd expect.
The math is simple but powerful: each period your balance grows by the periodic interest rate, then your next contribution is added. Repeat that for every month or year, and the line on the chart above curves upward — slowly at first, then noticeably faster. The longer your money compounds, the steeper that curve gets, which is why starting early matters so much more than starting big. The complete guide to how compound interest works walks through the period-by-period mechanism, why the curve bends, and where the Rule of 72 comes from.
What the numbers mean for you
The big number at the top is your projected balance. But the details underneath tell the real story. The interest split shows how much of your final total you actually deposited versus how much your money earned on its own — for long time horizons, the interest can dwarf your contributions.
The effective annual rate (APY) shows what your nominal rate is really worth once compounding is factored in, and the time-to-double figure is the famous Rule of 72 in action — at 7% a year, money roughly doubles every decade. Finally, the “in today's money” toggle adjusts for inflation, because a six-figure balance decades from now won't buy what six figures buys today. Seeing the real, inflation-adjusted value keeps the projection honest.
Frequently asked questions
How much is $10,000 in compound interest over 10 years?
At a 7% annual return, $10,000 left to compound for 10 years grows to roughly $19,670 — almost doubling — without adding a single extra dollar. Enter your own figures above to see the exact number and the year-by-year path.
Does money really double every 7 years?
Close — that's the Rule of 72. Divide 72 by your interest rate to estimate the doubling time. At about 10% a year money doubles in roughly 7 years; at 7% it's closer to every 10 years. The calculator shows your exact doubling time at the top.
Is investing $100 a month worth it?
Yes. Consistency beats size. $100 a month invested at 7% for 30 years becomes well over $100,000 — and most of that final total is interest, not the money you put in. Small, regular contributions are exactly what compounding rewards.
What is the Rule of 72?
It's a quick mental shortcut: 72 divided by your annual interest rate gives the approximate number of years for your money to double. It's surprisingly accurate for the rates most savers and investors see.
Worked examples
Each example below shows inputs fed directly into the compound interest engine. Every figure in the stat grid is computed at build time from those inputs, never hand-typed.
Consistent saver, 20 years
$5,000 starting balance, $200 added each month, at 7% annual rate compounded monthly for 20 years.
Total deposits of $53,000 grow to roughly $124,400 — the $71,400 gap is entirely interest. Interest accounts for 57% of the ending balance, illustrating why compounding rewards long time horizons.
Lump sum, 30 years
$10,000 invested as a one-time lump sum at 7% annually for 30 years, no additional contributions.
A $10,000 lump sum at 7% for 30 years grows to roughly $81,200 with no further deposits — the balance grows more than eightfold through compounding alone. Starting amount matters far less than starting time.
Aggressive growth, 10 years
$1,000 starting balance, $100/month at 10% rate for 10 years.
Depositing $13,000 total over 10 years results in roughly $23,200 — a $10,200 gain from interest alone. At 10%, the interest-to-contribution ratio continues to improve dramatically beyond 10 years.
Final balance: monthly contribution × annual rate at 20 years ($10,000 starting)
Each cell shows the projected balance after 20 years, starting from $10,000, at the given monthly contribution and annual rate.
| Monthly contribution | 5.0% | 7.0% | 8.0% | 10.0% |
|---|---|---|---|---|
| $0 | $27k | $40k | $49k | $73k |
| $100 | $68k | $92k | $108k | $149k |
| $200 | $109k | $145k | $167k | $225k |
| $300 | $150k | $197k | $226k | $301k |
| $500 | $233k | $301k | $344k | $453k |
At 7%, adding $200/month turns $10,000 into roughly $140k — vs $38k for the lump sum alone. Consistent contributions matter more than rate optimization.
What affects your results
These inputs move the needle most — ranked by their leverage on the final balance.
Time is the single most powerful variable in compound interest math. Doubling the time period more than doubles the ending balance at any positive rate, because compounding is exponential. An extra decade early in a savings journey outweighs a higher rate across a shorter period.
Regular contributions create a multiplier effect on compounding — each deposit becomes its own smaller investment that compounds from the moment it is added. Increasing contributions by $100/month over 20 years at 7% adds roughly $50,000 to the ending balance.
The rate determines how fast each dollar grows per period. A 1% rate difference (e.g., 6% vs 7%) over 20 years on $10,000 changes the ending balance by roughly $8,000. Rates matter, but their effect is smaller than time or consistent contributions on most realistic savings horizons.
A larger starting balance gives compounding a bigger base to work on from day one. But for most savers, contributions over time dwarf the starting principal. The biggest impact of a large starting amount is psychological — it makes the early years of compounding more visible.
Daily compounding vs monthly compounding on $10,000 at 5% for 10 years produces about $9 extra in interest. The difference between annual and monthly is larger but still under $200 on that horizon. Within savings accounts, chasing compounding frequency is the least leveraged optimization available.
Common mistakes to avoid
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Comparing nominal rates across accounts without converting to APY. A 5% nominal rate compounded monthly is actually a 5.12% APY — meaningfully different when comparing several accounts.
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Stopping contributions during a downturn. Pausing $200/month for one year early in a 30-year horizon can cost $10,000–$20,000 in ending balance through the lost compounding time, far more than the contributions themselves.
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Overestimating the impact of rate shopping. Moving from a 4.5% to 5.0% APY HYSA adds roughly $50/year per $10,000. That matters, but it is a fraction of the impact of consistent monthly contributions.
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Not accounting for inflation. A nominal $500,000 at retirement may represent $250,000 in today's purchasing power at 3% inflation over 25 years. Toggle the inflation adjustment to see real values.
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Treating the projected balance as a guarantee. Compound interest on savings accounts and CDs is reliable; on investments, the rate is an assumption, not a promise. Label your inputs accordingly.
Key takeaways
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Start now, not later. Ten extra years of compounding at 7% roughly doubles the ending balance regardless of rate or contribution size.
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Contributions over time beat a higher rate. Going from $200/month to $300/month adds more to a 20-year balance than raising the rate from 7% to 10%.
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Use APY, not nominal rate, when comparing savings accounts and CDs. The APY already accounts for compounding frequency.
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Toggle inflation to reality-check your goal. A projected $400,000 in 25 years represents about $200,000 of today's purchasing power at 3% inflation.
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The chart is more useful than the final number alone — the curve shows when compounding begins to visibly accelerate, which is the visual case for starting early.
Key terms
- Compound interest
- Interest calculated on the initial principal AND on the accumulated interest from previous periods. Because interest earns interest, balances grow exponentially — slowly at first, then accelerating as the base grows larger.
- APY (Annual Percentage Yield)
- The effective annual rate of return after accounting for compounding within the year. A 5% nominal rate compounded monthly produces an APY of about 5.12%. APY is always ≥ the nominal rate, and the two are equal only when compounding happens once per year.
- Nominal rate
- The stated annual interest rate before compounding effects are applied. Lenders and banks quote nominal rates; the APY is what you actually earn. For accurate projections, always confirm whether a rate is nominal or APY.
- Compounding frequency
- How often interest is calculated and added to the balance — annually, quarterly, monthly, or daily. More frequent compounding means interest earns interest sooner, increasing the effective yield (APY) slightly above the nominal rate.
- Rule of 72
- A mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes for money to double. At 6% the answer is 12 years; at 9% it is 8 years. It is surprisingly accurate for rates between 2% and 15%.
- Future value (FV)
- The projected worth of a current sum of money at a specified date in the future, given an assumed rate of growth. Future value is the output of compound-interest math — it tells you what a lump sum or stream of contributions will grow to.
- Real return (inflation-adjusted)
- The return on an investment after subtracting inflation. A 7% nominal return with 3% inflation gives a roughly 4% real return. Real return tells you how much your purchasing power actually grew — the number that matters for long-term goals.
- Time value of money
- The principle that a dollar today is worth more than a dollar in the future, because money available now can be invested and grow. Compound interest is the mechanism that quantifies exactly how much more a dollar today is worth.
More questions answered
How long does it take to turn $10,000 into $100,000?
It depends on your rate and whether you add contributions. At 7% with no contributions, $10,000 takes about 34 years to reach $100,000 (the Rule of 72 says it doubles every 10 years, so $10k → $20k → $40k → $80k → $100k+ is roughly 34 years). Add $200/month and you cross $100,000 in about 18 years instead. The calculator shows your exact timeline at the top of the results.
Is compound interest calculated daily or monthly?
It depends on the account. Most savings accounts and high-yield savings accounts compound daily but credit interest monthly. CDs typically compound daily or monthly. Investment accounts track returns continuously but report on a daily basis. The practical difference between daily and monthly compounding is tiny — under $10/year on a $10,000 balance at 5%. What matters far more is the rate and how long the money stays invested.
What is the difference between APY and interest rate?
The interest rate (nominal rate) is the stated annual percentage before compounding effects are applied. APY (Annual Percentage Yield) is what you actually earn over a year after compounding kicks in. A 5% nominal rate compounded monthly is a 5.12% APY. Banks are required to advertise savings rates as APY so consumers can compare fairly. When the calculator shows an "effective annual rate," that is the APY.
How much does $500 a month become in 30 years?
At 7% compounded monthly, $500 per month for 30 years grows to approximately $567,000 — from $180,000 in total deposits. At 8%, it reaches about $679,000. At 5%, about $417,000. The rate difference over 30 years is substantial: the gap between 5% and 8% on this scenario is about $260,000. Run the numbers in the calculator above for your exact rate and time horizon.
Does compounding work the same way on investments as on savings accounts?
The math is the same, but the rate input is different. Savings accounts and CDs have a stated rate that is contractually fixed. Investment accounts (stocks, index funds) produce returns that vary year to year. When using compound interest math for investing, you enter an assumed average annual return, not a guaranteed rate. Historically, diversified stock portfolios have returned about 7–10% annually before inflation, but any specific year can be positive or negative.
What rate of return should I use for long-term investing?
The S&P 500 has averaged roughly 10% annually in nominal terms and about 7% after inflation over long periods. For conservative assumptions, most financial planners use 6–7% for a diversified portfolio. For a high-yield savings account, use the current advertised APY — typically 4–5% in 2024–2025. Always label your projection with the assumed rate so you remember it is an estimate, not a guarantee.
What a balance this size looks like against US net worth
This projection reaches $124,379 after 20 years. For scale, here is how a balance of that size would compare today against median net worth by age — the Federal Reserve's 2022 Survey of Consumer Finances, published October 2023.
Read this as a reference point, not a scorecard. Net worth is everything a household owns minus everything it owes — home equity, vehicles, and every other account, less mortgage and other debts. The figure above is a single projected balance, so the two are not like-for-like: most households holding the median have much of it in home equity rather than an investment account. This is also a present-day comparison against 2022 figures, not a prediction of where you would rank in 20 years.
| Age of household head | Median net worth | This balance |
|---|---|---|
| Under 35 | $39,000 | above the median |
| 35–44 | $135,600 | below the median |
| 45–54 | $247,200 | below the median |
| 55–64 | $364,500 | below the median |
| 65–74 | $409,900 | below the median |
| 75 or older | $335,600 | below the median |
| All families | $192,900 | below the median |
A balance of $124,379 held today would sit above the median net worth of every age group up to and including under 35. Medians are used rather than averages throughout: net worth is heavily skewed by a small number of very large balances, so the mean for every bracket runs far above its median and describes almost nobody.
Source: Federal Reserve Bulletin, "Changes in U.S. Family Finances from 2019 to 2022," Vol. 109, No. 5 (October 2023), Table 2. Federal Reserve Bulletin (PDF). The 2022 SCF is the most recent published wave; the Fed surveys every three years.
Method and assumptions
This calculator projects a balance from the inputs you give it. It is an arithmetic model, not a forecast, and not financial advice — a real account’s return varies year to year while this projection holds your rate constant.
- Period-by-period, not a formula
- The balance is stepped forward one compounding period at a time rather than evaluated with a closed-form equation. That is what makes the year-by-year breakdown real numbers from the same run you see at the top, rather than a separate approximation.
- How the periodic rate is derived
- Your annual rate is divided by the number of compounding periods in a year — a 6% rate compounded monthly applies 0.5% each month. This is the standard convention, and it is why the nominal rate and the APY are not the same number: compounding those twelve 0.5% steps produces slightly more than 6% over the year.
- When contributions land
- Contributions are spread evenly across every compounding period and deposited at the end of each one, after that period’s interest has accrued — the ordinary-annuity convention most calculators use. Depositing at the start of each period instead would produce a slightly higher balance, so treat this projection as the conservative side of that choice.
- Inflation adjustment
- The “in today’s money” figures deflate the balance by your inflation rate compounded annually. Contributions are shown in the dollars you actually deposit, so the inflation-adjusted interest figure is the real terminal value minus what you put in — not a separately deflated interest total. See nominal versus real figures for the distinction.
- Time to double
- The doubling figure describes your rate alone — how long a balance takes to double with no further deposits. It deliberately ignores contributions, because mixing them in would measure your savings habit rather than the return; the Rule of 72 is the mental shortcut for the same number.
- What is not modelled
- Taxes, account fees, fund expense ratios, and any penalty for early withdrawal are all excluded. Returns are assumed constant rather than variable, so no sequence-of-returns risk is captured. A taxable account will trail these figures; a tax-advantaged one will track them more closely.