Methodology

Formulas

The calculator uses two standard compound-growth formulas:

Initial investment: FV = P × (1 + r/n)^(n × t)

Recurring contributions: FV = PMT × [((1 + r/n)^(n × t) − 1) / (r/n)]

The total projected future value is the sum of both results. Where P is the initial investment, PMT is the periodic contribution, r is the assumed annual return (as a decimal), n is the number of compounding periods per year, and t is the number of years.

Compounding frequency

Version 1 compounds monthly (n = 12) for both the initial investment and monthly contributions. This is a common simplification for modeling long-term stock market growth and does not imply that VOO's actual returns compound on any fixed schedule.

Contribution timing

Contributions are modeled as occurring at regular monthly intervals for the full duration of the investment period entered. The calculator does not currently support contributions that start partway through the period, one-time additional deposits, or withdrawals.

The zero-return case

When the assumed annual return is set to 0%, the formulas above would involve dividing by zero. The calculator detects this case and instead computes future value as simply the sum of the initial investment and all contributions, with no growth added — as you would expect at a 0% return.

Rounding

Year-over-year compounding is calculated at full floating-point precision — each year's ending balance carries forward unrounded into the next year's calculation, so rounding never accumulates across the projection. Rounding is only applied at the edges: to the nearest cent for the year-by-year table's individual figures, and to whole dollars for headline summary figures and the chart. Small differences of a dollar or two between the summary and the year-by-year table can occur because of this display-level rounding, not because of any loss of precision in the underlying calculation.

Input limits

To keep results meaningful and prevent calculation errors, the calculator enforces reasonable maximum values on dollar inputs, investment period (up to 75 years), and assumed annual return (between −20% and 30%). Values outside these ranges are rejected with an explanation rather than silently producing an invalid result.

What the core VOO calculator does not model

The formulas above describe the core VOO calculator (and the general-purpose calculators built on the same engine). Dividends specifically are modeled separately by the dedicated VOO dividend calculator, with reinvestment as an explicit on/off choice — not something the core calculator's single "assumed annual return" input does on its own. Its dividend growth rate assumption grows the dividend per share each year, not the yield directly: since yield is dividend ÷ price, the yield itself only rises if dividend growth outpaces your price return assumption, and falls if price growth outpaces it — an earlier version of this calculator compounded the growth rate directly into yield, ignoring price entirely, which overstated projected dividend income; that has been corrected.

The core calculator does not model:

• VOO's actual historical price or dividend data
• Inflation adjustment
• Taxes, brokerage fees, or fund expense ratios
• Contribution frequencies other than monthly
• Lump-sum additions or withdrawals partway through the plan

These are intentionally out of scope for the core calculator and are noted on the relevant pages as planned future enhancements, not implemented features.

Limitations

This calculator produces a mathematical projection based on assumptions you choose. It cannot predict what VOO, the S&P 500, or any other investment will actually return in the future. Actual results will differ — sometimes substantially — from any projection shown here. This tool is provided for educational purposes only and is not financial, investment, tax, or legal advice.