What the model calculates
Enter a starting balance, contribution, whole-number horizon (1–100 years), assumed annual mean return, volatility, and random seed. The preset pairs 6%/8%, 8%/12%, and 10%/18% are examples, not measured returns or investment recommendations.
For each of 5,000 paths, the calculator draws independent annual normal returns with a fixed mean and standard deviation. Returns below −100% are floored at −100%. The next balance is the prior balance multiplied by one plus that floored return, then the year-end deposit is added. Monthly contributions are multiplied by 12 and added at year end, so their within-year investment growth is omitted.
For a deterministic check, use $1,000 initially, $100 annual deposits, 10% mean return, zero volatility and two years. All paths end at $1,420: $1,000 × 1.1 + $100 = $1,200, then $1,200 × 1.1 + $100 = $1,420.
Reading the output
The sorted simulated balances provide the 10th, 50th and 90th percentiles at each year. The median is the middle simulated balance; it is not the arithmetic average, a promised compound rate, or a forecast. The lower and upper lines are not worst and best cases. Values outside the band remain possible, and each year’s percentile can represent a different simulated path.
What this leaves out
No historical prices, asset correlations, changing regimes, withdrawals, taxes, fees, inflation or retirement target are modeled. Independent normal draws can miss clustered volatility and extreme tails; flooring losses changes the distribution. More simulated paths do not validate these assumptions. Compare different assumptions rather than treating the band as a safety guarantee.
The normal-distribution mean and standard-deviation definitions are documented in the NIST statistical handbook. That mathematical reference does not establish that market returns follow this model.
Frequently Asked Questions
What does annual volatility mean here?
It is the standard deviation of the assumed annual normal return draw, in percentage points. About 68% of an unclipped normal distribution lies within one standard deviation of its mean. This is a model assumption, not a statement about actual market returns.
Are the 10th and 90th percentiles the worst and best outcomes?
No. They are pointwise simulated percentiles. About 10% of samples lie below the lower percentile and 10% above the upper one. The shaded band is not a guaranteed range, a confidence interval for a forecast, or a path that one portfolio necessarily follows.
Does this use historical prices or calculate retirement success?
No. The presets are illustrative inputs, not historical estimates or recommended portfolios. The model has no withdrawals, retirement target, tax, fees, inflation, changing volatility, or asset correlations.
How are contributions and losses handled?
Monthly contributions are multiplied by 12 and deposited at year end; there is no monthly compounding of those deposits. A drawn return below minus 100% is floored at minus 100% before the annual deposit. This simplified loss floor changes the normal distribution, especially with extreme inputs.