Compound Interest Calculator
See how your money grows over time with compound interest. Visualize the power of compounding with monthly contributions.
Compound interest is often summarized as 'interest on interest': each period's earnings get added to the balance and then themselves start earning a return, so growth accelerates rather than staying flat the way simple interest would. This calculator runs that compounding explicitly, period by period, for however many times per year you select — daily, monthly, quarterly, or annually — adding your monthly contribution (pro-rated to match the compounding frequency) at each step. Compounding frequency changes two things here, not one. First, for a given nominal annual rate, compounding more often produces a higher Effective Annual Rate, because interest starts earning its own interest sooner. Second -- and usually the larger effect -- your contributions are pro-rated to the compounding period, so choosing Annually deposits a full year's worth of contributions in one lump at year end rather than spreading it across twelve monthly deposits, and that money loses a year of growth each cycle. At the default settings, switching from Annually to Monthly raises Future Value by about $22,600, of which only about $2,700 comes from the higher effective rate; the rest is purely contribution timing. If you contribute monthly in real life, leave the frequency on Monthly. Time Period also tends to matter more than frequency at typical rates, because the compounding effect itself grows with the number of periods, not just their spacing — a 30-year horizon at a modest rate typically outgrows a 10-year horizon at a considerably higher one — at the default contribution, 30 years at 5% beats 10 years at 20%, though a truly extreme rate can still close the gap. The Effective Annual Rate output translates your nominal rate and chosen compounding frequency into the single annualized rate that would produce the same growth if compounded just once a year, letting you compare across different compounding schedules on equal footing. What this calculator does not model: variable or negative-return years (a constant rate is assumed throughout), taxes on investment gains, or account fees that would erode the stated return.
Financial Disclaimer
This calculator is for educational purposes only and does not constitute financial advice. Results are estimates based on the inputs provided. Consult a qualified financial advisor before making investment or financial planning decisions.
Inputs
Typical: $1K–$50K
Typical: $100–$2,000/mo
Typical: 5–10% for index funds
Typical: 10–30 years
Results
Future Value
$343,778.24
≈ 8 Teslas
Compound growth with regular contributions
- 1.Convert the annual rate to a rate per compounding period
Interest is credited once per period, so the annual percentage has to be divided down to the period it is actually applied over.
- 2.Grow the starting balance
The money already invested compounds untouched for the whole term — this part behaves exactly like a lump sum left alone.
- 3.Sum the growth of every contribution
Each deposit compounds for a different length of time — the first for almost the whole term, the last for none of it. Adding those up is a geometric series, and this fraction is its closed form. It is the same series that amortises a mortgage, read forwards instead of backwards.
- 4.Add the two together
The two parts are independent — what the original sum became, plus what the deposits became — so the total is simply their sum.
The present-value-of-an-annuity relationship this inverts appeared in Simon Stevin's printed interest tables, and Richard Witt's Arithmeticall Questions extended it to series of payments in English three decades later.
How to Use This Calculator
- Enter your Initial Investment (the lump sum you're starting with).
- Set a Monthly Contribution if you plan to add money regularly.
- Enter the expected annual Interest Rate (stock market averages ~8-10%).
- Choose the number of Years you plan to invest.
- Select the Compounding Frequency (monthly is most common for investments).
- Review the growth chart and final balance to see how compounding accelerates over time.
How the result changes with Time Period
| Time Period | Future Value |
|---|---|
| 5.9 | $60,337.17 |
| 18 | $282,048.81 |
| 33 | $1,105,732.36 |
| 45 | $2,998,905.94 |
What each input means
- Initial Investment
- Lump sum amount you're starting with today.
- Monthly Contribution
- Amount you'll add each month going forward.
- Annual Interest Rate
- Historical S&P 500 average is about 10% before inflation.
- Time Period
- How long you plan to invest.
- Compounding Frequency
- How often interest is calculated and added to your balance.
How this is calculated
Worked example, using the default values
- Effective Annual RateEAR = (1 + r/n)ⁿ − 1(1 + 8.0% / 12)^12 − 1 = 8.30%
- Total ContributionsContributions = Initial + (Monthly × 12 × Years)$10,000.00 + ($500.00 × 12 × 20) = $130,000.00
- Future ValueFV = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) / (r/n)]Computed iteratively over 240 compounding periods = $343,778.24
- Total Interest EarnedInterest = Future Value − Total Contributions$343,778.24 − $130,000.00 = $213,778.24
Engine last updated .
Frequently Asked Questions
How much does compounding frequency actually change my results?
It depends heavily on your rate. At a modest rate the difference is small — at 1%, switching from annual to daily compounding moves the default projection by well under a percent. At 8% it is about 8%. At the top of this calculator's range, 30%, switching from annual to daily more than doubles the projected balance. Part of that is compounding itself, and part is that your contributions get deposited on the compounding schedule, so annual compounding also means annual (rather than monthly) deposits. If you contribute monthly in practice, leave the setting on Monthly so the timing matches reality.
What is the Effective Annual Rate and how is it different from my entered interest rate?
Your entered Annual Interest Rate is the nominal rate; Effective Annual Rate is what that nominal rate actually works out to once compounding is applied at your chosen frequency, expressed as a single annualized figure. It's always slightly higher than the nominal rate for any compounding frequency more often than annual, because compounding lets interest earn interest within the year rather than only once at year-end.
Is the historical ~10% S&P 500 average return a realistic rate to plug in here?
It's a commonly cited long-run historical average for US large-cap stocks before adjusting for inflation, but any single year (or even decade) can differ substantially from that average, and past performance doesn't guarantee future results. Many planners use a more conservative rate — often in the 6-8% range — to build in a margin of safety, especially for money needed within a shorter time horizon.
How does a monthly contribution affect the calculation compared to just the initial investment?
Regular monthly contributions add new principal at every compounding period, so each contribution gets fewer total years to compound than the initial lump sum did, but the combined effect of many contributions over time is still substantial — consistent monthly investing is often what drives the bulk of a long-term balance's growth, not just the size of the starting lump sum.
Does this calculator account for market downturns or a bad year of returns?
No — it applies one constant rate of return across every compounding period for the entire time horizon, smoothing out the real ups and downs markets experience year to year. A portfolio that experiences the same average return but with a poor sequence of early losses can end up meaningfully different from this smooth projection, a risk known as sequence-of-returns risk.
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