What return rate should I use for stock market projections?

The S&P 500 has returned approximately 10.3% annually (nominal) since 1926 and about 7% after inflation. For conservative planning, we recommend using 7-8% nominal (4-5% real) for a diversified stock portfolio. For a balanced portfolio (60% stocks / 40% bonds), use 6-7% nominal. These figures assume broad index fund investing with low fees. If you plan to use the projection for critical financial decisions like retirement timing, consider using a lower rate (6% nominal) to build in a safety margin against poor sequence-of-returns outcomes.

How much difference does compounding frequency make?

The difference between annual and monthly compounding is relatively small but grows with time and rate. For a $10,000 investment at 8% over 30 years: annual compounding yields $100,627, while monthly compounding yields $109,357 — a 8.7% difference. At higher rates or longer time horizons, the gap widens further. Daily compounding (365x/year) adds only about $200 more than monthly over the same period. For practical purposes, the jump from annual to monthly compounding matters most; going beyond monthly produces negligible additional returns.

Is the 4% rule still valid for retirement planning?

The 4% rule (and its corresponding 25x FIRE number) remains a widely cited starting point, but it has been debated extensively since the original Trinity Study. Updated research by Wade Pfau, Michael Kitces, and others suggests that 4% is still reasonable for 30-year retirements when starting from moderate market valuations and maintaining a 50-75% stock allocation. However, for early retirees with 40-50 year time horizons, a more conservative 3.0-3.5% withdrawal rate (28-33x expenses) provides a larger safety margin. Market valuation at the time of retirement is the single biggest predictor of safe withdrawal rates.

How does the Gordon Growth Model handle changing dividend growth rates?

The basic Gordon Growth Model assumes a constant dividend growth rate in perpetuity, which is its primary limitation. In practice, many companies experience different growth phases: rapid growth early on, decelerating growth as they mature, and stable growth at maturity. A two-stage or three-stage dividend discount model handles these transitions by applying different growth rates to different time periods. Our calculator uses the single-stage Gordon model for simplicity but recommends it primarily for mature, stable-dividend companies with predictable growth, such as utilities, REITs, and blue-chip dividend aristocrats.

Why do my actual investment returns differ from the calculator projection?

The most common reasons are: (1) Volatility drag — in real markets, a 20% loss followed by a 25% gain does not return you to even (it leaves you at 100%), and this drag reduces the geometric (actual) return below the arithmetic (average) return used by most calculators; (2) Fees — fund expense ratios, trading commissions, and advisory fees compound negatively just as returns compound positively, and even a 1% annual fee can reduce a 30-year portfolio by 25%; (3) Behavioral factors — research consistently shows individual investors earn 2-4% less annually than the funds they hold due to poor timing of buys and sells; (4) Taxes — in taxable accounts, annual tax drag on dividends and realized gains reduces effective compounding.

Updated: 2026-02-07·14 min read read

Investment Growth Formulas: How We Calculate Returns

Building long-term wealth through investing depends on a handful of powerful mathematical concepts: compound interest, regular contributions, tax-advantaged growth, and inflation adjustment. Our <a href="/finance/investment-calculator" class="text-blue-600 hover:underline">investment calculator</a> and <a href="/finance/compound-interest-calculator" class="text-blue-600 hover:underline">compound interest calculator</a> implement these formulas with precision, but we believe you should understand exactly how every number is derived. This methodology page documents each formula, explains the underlying assumptions, and works through concrete examples.

The core principle behind all investment growth calculations is compounding — the process by which investment returns generate their own returns over time. Albert Einstein reportedly called compound interest the eighth wonder of the world, and the math justifies the claim. An investment growing at 8% annually does not simply gain 80% over 10 years; it gains 115.9% because each year's return is earned on a progressively larger base. This exponential growth is what makes time the most powerful variable in investing.

Beyond basic compounding, our calculators model regular contributions (dollar-cost averaging), inflation erosion, different compounding frequencies, tax drag, and goal-based projections like FIRE (Financial Independence, Retire Early) numbers. Each formula below is presented in plain language with fully worked examples so you can verify our math or replicate the calculations in a spreadsheet.

Formulas & Equations

Compound Interest

A = P x (1 + r/n)^(n x t)

This is the foundational formula for investment growth without additional contributions. It calculates the future value of a lump-sum investment compounded at a fixed rate over time. The key insight is that interest is earned on prior interest, creating exponential growth. Compounding frequency (n) matters: monthly compounding produces slightly more wealth than annual compounding at the same nominal rate because interest begins earning interest sooner.

Variables:

A = The future value of the investment, including all accumulated interest
P = The principal — the initial amount invested at time zero
r = The annual nominal interest rate expressed as a decimal (e.g., 0.08 for 8%)
n = The number of times interest is compounded per year (1 = annually, 12 = monthly, 365 = daily)
t = The investment duration in years

Future Value with Regular Contributions

FV = P x (1 + r/n)^(n x t) + C x [((1 + r/n)^(n x t) - 1) / (r/n)]

This extended formula adds the power of regular periodic contributions to the base compound interest calculation. The first term computes the growth of the initial principal, identical to the standard compound interest formula. The second term computes the future value of an annuity — the accumulated value of all periodic contributions, each compounding for a different duration. The result is the total portfolio value at the end of the investment horizon.

Variables:

FV = Total future value of the investment including initial principal growth and all contributions with their accumulated interest
P = The initial principal invested at time zero
C = The fixed contribution amount made at the end of each compounding period (e.g., $500/month if n = 12)
r = Annual nominal return rate as a decimal
n = Compounding frequency per year (matches the contribution frequency)
t = Total investment duration in years

Real Return (Inflation-Adjusted)

Real Return = ((1 + Nominal Return) / (1 + Inflation Rate)) - 1

Nominal returns overstate the actual purchasing power growth of an investment because inflation erodes the value of future dollars. The real return formula adjusts for this by removing the inflationary component from the nominal return. This relationship is known as the Fisher equation. For example, an 8% nominal return during a period of 3% inflation yields a real return of approximately 4.85%, not the 5% that simple subtraction would suggest. Our calculator uses the exact Fisher formula rather than the approximate subtraction method.

Variables:

Real Return = The inflation-adjusted annual return, representing actual purchasing power growth
Nominal Return = The stated annual return before adjusting for inflation, expressed as a decimal
Inflation Rate = The annual rate of consumer price increase, expressed as a decimal (e.g., 0.03 for 3%)

FIRE Number (Financial Independence Target)

FIRE Number = Annual Expenses x 25

The FIRE number represents the investment portfolio size needed to sustain a given lifestyle indefinitely through investment withdrawals. The "25x rule" is derived from the 4% safe withdrawal rate (SWR), which originated from the Trinity Study (Cooley, Hubbard, and Walz, 1998). If you withdraw 4% of your portfolio annually, you need 1/0.04 = 25 times your annual expenses saved. The 4% rule was designed to provide a high probability (approximately 95%) that a portfolio of 50-75% stocks and 25-50% bonds would survive a 30-year retirement without depletion.

Variables:

FIRE Number = The portfolio value required to achieve financial independence, allowing you to live off investment returns
Annual Expenses = Your total yearly spending in retirement, including housing, food, healthcare, taxes, insurance, and discretionary spending
25 = The inverse of the 4% safe withdrawal rate; using a 3.5% SWR yields a 28.6x multiplier for more conservative planning

Dividend Growth Model (Gordon Growth Model)

Fair Value = D1 / (r - g)

The Gordon Growth Model estimates the intrinsic value of a stock (or portfolio) based on its expected future dividend stream growing at a constant rate in perpetuity. D1 is next year's expected dividend, r is the required rate of return, and g is the expected constant growth rate of dividends. This model is most applicable to mature, dividend-paying companies with stable growth rates. Our calculator uses it to estimate the long-term income stream and terminal value of dividend-focused portfolios.

Variables:

D1 = The expected dividend payment in the next period (typically next year's annual dividend per share)
r = The investor's required rate of return (discount rate), reflecting the opportunity cost and risk premium
g = The expected constant annual growth rate of dividends, which must be less than r for the formula to produce a valid result

Step-by-Step Process

Step 1: Define the Investment Parameters

The calculator begins by collecting the core inputs: initial investment amount (principal), regular contribution amount and frequency, expected annual return rate, investment time horizon, and compounding frequency. Each input includes a sensible default value based on common assumptions — 8% annual return for a diversified stock portfolio, monthly contributions, and monthly compounding.

Users can optionally specify an inflation rate (default 3% based on long-term U.S. average) and a tax rate on investment gains. These optional parameters enable the calculator to display both nominal and inflation-adjusted results, as well as pre-tax and after-tax projections.

Example:

A user enters: $10,000 initial investment, $500 monthly contributions, 8% annual return, 30-year time horizon, monthly compounding, 3% inflation.

Step 2: Calculate Future Value with Compounding

The calculator applies the future value formula with regular contributions. The initial $10,000 grows according to the compound interest formula: P x (1 + r/n)^(nt). Simultaneously, each monthly $500 contribution begins compounding from the date it is made. The contribution component uses the future value of an annuity formula.

The total future value is the sum of the compounded principal and the compounded contributions. Our calculator breaks this down in the output so users can see how much of the final balance came from their contributions versus how much came from investment growth (the "free money" of compounding).

Example:

For $10,000 initial + $500/month at 8% for 30 years: Principal growth = $10,000 x (1.00667)^360 = $109,357. Contribution growth = $500 x [((1.00667)^360 - 1) / 0.00667] = $745,180. Total = $854,537. Total contributions were $190,000 ($10,000 + $500 x 360), meaning $664,537 came from compounding.

Step 3: Adjust for Inflation

To show results in today's purchasing power, the calculator deflates the nominal future value using the specified inflation rate. This is done by dividing the nominal future value by (1 + inflation)^t. Alternatively, users can view the real return by applying the Fisher equation to the nominal return rate before calculating, which produces the same result.

Inflation adjustment is crucial for long time horizons. Over 30 years at 3% inflation, a dollar today is worth approximately $0.41 in future purchasing power. The $854,537 nominal portfolio from our example has a real (inflation-adjusted) purchasing power of roughly $352,000 in today's dollars — still impressive, but a very different number.

Example:

Nominal FV = $854,537. Inflation-adjusted FV = $854,537 / (1.03)^30 = $854,537 / 2.4273 = $352,025 in today's dollars.

Step 4: Generate Year-by-Year Breakdown

The calculator generates a year-by-year (and optionally month-by-month) table showing the portfolio value at the end of each period. For each row, it displays the beginning balance, contributions made during the period, investment return earned, and ending balance. A cumulative total of contributions versus earnings is maintained so users can visualize the crossover point where investment growth exceeds total contributions.

This breakdown is particularly valuable for demonstrating the power of compounding over time. In the early years, contributions dominate growth. In later years, investment returns overwhelm contributions. In our example, the crossover occurs around year 14, after which investment returns in a single year exceed the $6,000 in annual contributions.

Example:

Year 1: Start $10,000 + $6,000 contributions + $888 growth = $16,888. Year 15: Start $145,230 + $6,000 contributions + $11,618 growth = $162,848. Year 30: Start $784,920 + $6,000 contributions + $63,617 growth = $854,537.

Step 5: Calculate FIRE and Milestone Projections

If the user enters annual expenses, the calculator computes the FIRE number (25 x annual expenses) and estimates how many years until the portfolio reaches that target. It solves for t in the future value equation using numerical methods (Newton-Raphson iteration) since the equation with regular contributions cannot be solved algebraically for t.

The calculator also identifies milestone dates: when the portfolio first reaches $100K, $250K, $500K, and $1M. These milestones help users set intermediate goals and celebrate progress along the way. Each milestone displays both the estimated date and the total contributions made up to that point.

Example:

For $40,000 annual expenses: FIRE Number = $40,000 x 25 = $1,000,000. With $10,000 initial and $500/month at 8%, the portfolio reaches $1M in approximately year 33. The $100K milestone is reached around year 7, and $500K around year 24.

Step 6: Present Results with Visualizations

The final output includes multiple views: a summary card showing the end balance (nominal and real), total contributions, total investment growth, and effective annual return; a growth chart plotting portfolio value over time with contributions stacked against earnings; and a detailed table with year-by-year or month-by-month data that can be exported to CSV.

We also show a comparison panel where users can see how changing any single variable (return rate, contribution amount, time horizon) affects the final outcome. For example, the impact of starting 5 years earlier, contributing an extra $100/month, or earning 1% more annually. These comparisons illustrate the sensitivity of long-term outcomes to small changes in inputs.

Example:

Starting 5 years earlier (35 years instead of 30) increases the final balance from $854,537 to $1,305,024 — a 52.7% increase from just 5 additional years of compounding, demonstrating why starting early is the single most impactful investing decision.

Assumptions and Limitations

Our investment calculator assumes a constant annual return rate throughout the investment period. In reality, market returns are volatile — the S&P 500 has returned anywhere from -37% (2008) to +33% (2013) in a single year. The average nominal return of the S&P 500 since 1926 is approximately 10.3%, but this average masks enormous year-to-year variability. Using a fixed rate produces a smooth exponential growth curve that is useful for planning but does not reflect the actual experience of investing, which involves significant drawdowns and recoveries.

The calculator also assumes contributions are made at regular intervals without interruption. In practice, job changes, emergencies, and life events may force investors to pause or reduce contributions temporarily. The impact of missed contributions is asymmetric: missing contributions early in the investment horizon has a larger impact on the final balance than missing contributions later, because early contributions have more time to compound.

Tax treatment is simplified in our standard model. In taxable accounts, dividends and realized capital gains are taxed annually, creating "tax drag" that reduces the effective compound rate. In tax-advantaged accounts (401k, IRA, Roth IRA), different rules apply depending on the account type. Our calculator offers a basic tax-rate adjustment but does not model the full complexity of tax-loss harvesting, required minimum distributions, or the differences between traditional and Roth account structures.

Monte Carlo vs. Deterministic Projections

Our standard calculator uses a deterministic model — it applies a single fixed return rate to produce a single projected outcome. This approach is intuitive and useful for goal-setting, but it can create false confidence by suggesting a precise future balance. In reality, the range of possible outcomes is wide. A portfolio with an expected 8% return and 15% standard deviation could plausibly grow to anywhere between $400,000 and $2,000,000 over 30 years depending on the sequence of returns.

Monte Carlo simulation addresses this limitation by running thousands of randomized scenarios using historical return distributions. Each simulation randomly assigns annual returns drawn from a statistical distribution (typically lognormal with parameters based on historical data) and tracks the portfolio through time. The result is a probability distribution of outcomes rather than a single number — for example, a 50th percentile outcome of $800,000, a 10th percentile (bad luck) outcome of $450,000, and a 90th percentile (good luck) outcome of $1,500,000.

We are developing a Monte Carlo feature for our advanced investment calculator. In the meantime, users can approximate outcome ranges by running the deterministic calculator multiple times with different return assumptions: a base case (8%), a conservative case (6%), and an optimistic case (10%). The spread between these scenarios gives a rough sense of the uncertainty involved, though it understates tail risks compared to a full Monte Carlo analysis.

Tax Impact Considerations

Taxes are the single largest drag on investment returns for most investors, yet they are often overlooked in basic calculators. In a taxable brokerage account, dividend income is taxed annually at either ordinary income rates (for non-qualified dividends) or the qualified dividend rate (0%, 15%, or 20% depending on income). Capital gains are taxed upon realization — when you sell an investment for a profit. Long-term capital gains (held over one year) receive preferential rates, while short-term gains are taxed as ordinary income.

Tax-advantaged accounts offer significant benefits. Traditional 401(k) and IRA contributions are tax-deductible, meaning you invest pre-tax dollars that grow tax-deferred. You pay ordinary income tax only upon withdrawal in retirement, ideally at a lower tax bracket. Roth accounts work in reverse: contributions are made with after-tax dollars, but all growth and qualified withdrawals are completely tax-free. For a 30-year investment horizon, the difference between taxable and Roth growth can be 20-40% in final account value.

Our calculator's optional tax field applies a simplified annual tax drag to model taxable accounts. It reduces the effective compound rate by the specified tax rate multiplied by the portion of the return that would be taxable. For a more thorough tax analysis, users should consult a tax professional or financial advisor who can model their specific situation, including state taxes, the net investment income tax (3.8% for high earners), and the interaction between retirement account distributions and Social Security taxation.