Finance

Compound Interest Calculator

Calculate compound interest with monthly contributions. See end balance, total interest earned, and a year-by-year breakdown using the A=P(1+r/n)^(nt) formula.

  • Internal Revenue Service data · June 2026
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Data updated: · Source: IRS Publication 550 — Investment Income and Expenses
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How to use this calculator

Follow this tool’s steps, then review its formula, assumptions, and limits below.

Step by step
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Compound interest is the engine behind long-term wealth building — your interest earns interest. This calculator applies the standard compound interest formula with optional recurring monthly contributions, so you can model savings accounts, CDs, investment portfolios, or retirement funds. Enter your principal, rate, and time horizon to see exactly how your money grows.

When to use this calculator

  • Projecting the future value of a savings or money-market account
  • Modeling retirement portfolio growth with regular contributions
  • Comparing daily vs. monthly vs. annual compounding frequencies
  • Estimating how long it takes a lump sum to double at a given rate
  • Evaluating CD or high-yield savings account offers side by side
  • Planning an education fund with monthly deposits over 10–18 years

Compounding Frequency Comparison — $10,000 at 7% Annual Rate, 10 Years, No Contributions

Compounding FrequencyPeriods per Year (n)End Balance
Annually1$19,672
Quarterly4$19,889
Monthly12$20,097
Daily365$20,137

Fuente: Worked example included in this calculator's methodology, consistent with FDIC Regulation DD compounding disclosure standards (2025).

How it works

What is Compound Interest?

Compound interest is the interest earned on both your initial investment and accumulated interest over time, creating exponential growth. Using the formula FV = P(1+i)^n, your money accelerates as interest generates additional interest. Time is the most powerful factor: doubling your investment horizon typically more than doubles your final amount.

What is Compound Interest?

Compound interest is the process where interest earned on your principal balance generates additional interest, creating exponential growth over time. The formula A=P(1+r/n)^(nt) calculates the final amount. For example, $10,000 at 7% annual interest grows to $76,123 in 30 years without contributions. With regular monthly additions, growth accelerates significantly through reinvestment cycles.

How Compound Interest Works

Compound interest calculates returns on both your original principal and the accumulated interest from prior periods. The more frequently interest compounds, the faster the balance grows — this is the core mechanic that makes early investing so powerful.

Formula

For a lump sum with regular contributions:

A = P·(1 + r/n)^(n·t)  +  PMT·[(1 + r/n)^(n·t) − 1] / (r/n)

Where:

  • A = End balance

  • P = Initial principal

  • r = Annual interest rate (decimal, e.g. 0.07 for 7%)

  • n = Compounding periods per year (1, 4, 12, or 365)

  • t = Time in years

  • PMT = Monthly contribution (converted to per-period amount)

    • When contributions are monthly and compounding is not monthly, the monthly contribution is adjusted: contributions are summed over each compounding period and treated as a single deposit at period end.

    Worked Example

    InputValue
    Principal$10,000
    Monthly contribution$200
    Annual rate7%
    Years20
    CompoundingMonthly (n=12)

    Step 1 — Lump-sum portion:

    10,000 · (1 + 0.07/12)^(12·20) = 10,000 · (1.005833)^240 ≈ $40,064

    Step 2 — Contribution portion (PMT per period = $200):
    200 · [(1.005833)^240 − 1] / 0.005833 ≈ $104,185

    Step 3 — End balance: $40,064 + $104,185 = $144,249
    Total contributions: $10,000 + ($200 × 240) = $58,000
    Total interest: $144,249 − $58,000 = $86,249

    Compounding Frequency Comparison (7%, 10 years, $10K principal, no contributions)

    Daily compounding earns ~$465 more than annual over 10 years on $10,000 — meaningful, but not dramatic at moderate rates.

    Limitations & When Not to Apply

  • Tax drag not modeled. Taxable accounts reduce effective returns; use tax-advantaged accounts (401k, IRA, Roth) for more accurate retirement projections.

  • Fixed rate assumed. Market returns fluctuate; this formula is best suited for fixed-rate products (savings accounts, CDs) or long-run average projections.

  • Contributions assumed at period end. If your account credits contributions at month start, actual results will be marginally higher.

  • Inflation not adjusted. The end balance is in nominal dollars; purchasing power may be lower in real terms.

  • No fees or expense ratios. For investment funds, subtract annual fees (e.g., 0.05%–1%) from the stated rate for a realistic estimate.

    • Example: $10,000 plus $200/month for 20 years at 7%

    Total contributions: $10,000 principal + ($200 × 240 months) = $58,000 of your own money
    Compound growth: monthly compounding at 7% over 20 years adds interest on interest
    Interest earned: $144,572.72 end balance − $58,000 contributed = $86,572.72
    The account grows to $144,572.72, of which about 60% ($86,572.72) is compound interest you never deposited. Figures as of Jun 2026.
    Disclaimer: Informational estimate. Actual rates, fees, and terms depend on the provider and contract; compare official documents before deciding.

    Frequently asked questions

    What is compound interest vs. simple interest?
    Simple interest applies the rate only to the original principal. Compound interest applies the rate to the principal plus all previously earned interest. On $10,000 at 7% for 10 years: simple interest yields $17,000; monthly compounding yields $20,097 — a $3,097 difference.
    How much does compounding frequency actually matter?
    At typical savings rates (1–7%), the difference between monthly and daily compounding is small — often under 0.1% of the end balance. The frequency matters most at higher rates and over longer periods. Choosing a higher rate matters far more than maximizing compounding frequency.
    What annual rate should I use for a stock market projection?
    The U.S. stock market (S&P 500) has returned roughly 10% nominal or about 7% inflation-adjusted annually over long periods. Financial planners commonly use 6–8% for conservative long-term projections. Past performance does not guarantee future results.
    Does this formula work for a savings account with a stated APY?
    Yes, but use APY (Annual Percentage Yield) directly as your annual rate with n=1 (annual compounding). APY already accounts for the bank's compounding schedule, so there is no need to select a different frequency — doing so would double-count the compounding effect.
    How are monthly contributions handled when compounding is quarterly or daily?
    The calculator accumulates monthly contributions within each compounding period and treats the sum as a single deposit at period end. This is a standard approximation. For most practical purposes the difference from a more exact method is less than 0.5%.
    Why does the year-by-year breakdown show accelerating growth?
    Each year, interest is earned on a larger base — both your deposits and all prior interest. This acceleration is the compounding effect. In early years most growth comes from contributions; in later years, interest on accumulated balances dominates.
    What is the Rule of 72?
    The Rule of 72 estimates the number of years needed to double a lump sum: divide 72 by the annual rate. At 6%, money doubles in roughly 12 years (72÷6=12); at 9%, about 8 years. It is a quick mental check, not a substitute for this calculator.
    How do I account for annual increases in my monthly contribution?
    This calculator assumes a fixed monthly contribution. For step-up or inflation-adjusted contribution modeling, run multiple scenarios manually — increase the PMT in 5-year increments and note the cumulative balance at each milestone as a starting principal for the next segment.
    Is compound interest taxable?
    In the U.S., interest income in taxable accounts is generally taxed as ordinary income in the year it is credited, per IRS Publication 550. In tax-deferred accounts (Traditional IRA, 401k), taxes are postponed until withdrawal. In Roth accounts, qualified withdrawals are tax-free.
    What's the difference between APR and APY?
    APR (Annual Percentage Rate) is the stated rate before compounding. APY (Annual Percentage Yield) reflects the effective return after compounding within the year. A 12% APR compounded monthly equals a 12.68% APY. Banks must disclose APY under the Truth in Savings Act.

    Sources & references

    Methodology & trust

    Editorial

    Finance calculator with its formula verified automatically against IRS Publication 550 — Investment Income and Expenses, per our editorial policy and methodology.

    Updates

    Updated: June 2026. Parameters are verified periodically against the cited sources.

    Privacy

    Calculations run 100% in your browser. We do not store or transmit your data.

    Limitations

    Indicative results. For critical decisions, consult a professional.

    📌 How to cite this calculator

    Rodríguez, M. (2026). Compound Interest Calculator. Hacé Cuentas. https://hacecuentas.com/en/compound-interest-calculator

    Content licensed under CC-BY 4.0 — reuse it citing the source with a link to Hacé Cuentas.

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