Retirement plan Monte Carlo
One projection is a single path through a random future. This engine runs the same household plan hundreds of times with different return sequences and reports how often it survives, where the ending balance actually lands, and how much the answer depends on volatility.
| Percentile | Ending net worth |
|---|---|
| Worst | $0.00 |
| 10th | $0.00 |
| Median | $3,706,712 |
| 90th | $18,769,553 |
| Best | $98,570,099 |
A wide p10–p90 band means the plan depends heavily on the return sequence.
r_t = μ + σ·z_t · Independent normal draws, seeded for reproducibility.
same projection engine · Tax, drawdown and account order are unchanged per path.
balance ≥ 0 at every age · A path fails the first year it hits zero.
A clear path from inputs to results.
One projection is a single path through a random future. This engine runs the same household plan hundreds of times with different return sequences and reports how often it survives, where the ending balance actually lands, and how much the answer depends on volatility.
How to use
- Enter the household and its spending.
- Set the expected return and volatility.
- Choose the number of paths and a seed.
- Read the success rate and the percentile band.
The formula
Reference: Monte Carlo simulation with independent normal annual returns, replayed by the household projection engine on the accumulation identity (Broverman, Mathematics of Investment and Credit).
Worked example
Age 45 to 95, $1.3M saved, $80,000 spending, 12% volatility
- Age 45, retire 65, plan to 95.
- Taxable $300k, deferred $900k, Roth $100k.
- Income $120k, spending $80k.
- Return 6%, volatility 12%, 200 paths, seed 7.
- 1
Each of the 200 paths draws an annual return from a normal distribution around 6%.
- 2
Every path replays the same tax and drawdown engine.
- 3
127 of the 200 paths survive to age 95: a 63.5% success rate.
- 4
Median ending balance $3.71M; 10th percentile $0; 90th percentile $18.77M.
- 5
The deterministic single-path projection sits inside this distribution, not at its centre by definition.
63.5% success · median $3.71M · p10 $0 · p90 $18.77M.
Interpreting the result
A 63.5% success rate is not a coin flip on your life; it is the share of simulated futures in which the plan did not run out. The gap between the median and the 10th percentile is the real message: the same plan can end with $3.7M or nothing depending on the order and size of returns, which is exactly what a single deterministic line hides.
Assumptions & limitations
- Independent normal annual returns; no fat tails or serial correlation.
- The same tax and drawdown rules as the deterministic plan.
- Constant inflation.
- Paths are seeded, so a quoted result can be reproduced exactly.
Frequently asked questions
Why is the success rate lower than my projection?
The projection assumes one average return every year. Volatility alone reduces survival, even with the same average.
How many paths should I run?
200–400 is enough for a planning decision; more paths reduce sampling noise, not model error.
What does the seed do?
It fixes the random sequence. The same seed and inputs always produce the same result.
Methodology last reviewed 2026-10-21. Results are informational and not financial or engineering advice — see our disclaimer.