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

All dollar figures are calculated in full precision internally and rounded to whole dollars for display in summary figures and the chart, and to the nearest cent internally between calculation steps. Small rounding differences of a dollar or two between the summary and the year-by-year table can occur due to this rounding.

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 Version 1 does not model

• VOO's actual historical price or dividend data
• Automatic dividend reinvestment as a separate mechanism from the assumed return
• 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 Version 1 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.