Year-by-year simulation of both paths, a price-to-rent sanity check, the break-even year, and a Monte Carlo probability instead of a single misleading answer.
| Monthly mortgage payment (principal and interest) | — |
| Price-to-rent ratio | — |
| Year 1 cost of owning | — |
| Year 1 cost of renting | — |
| Home value at the end | — |
| Mortgage balance remaining | — |
| Equity if you buy | — |
| Portfolio if you rent and invest | — |
| In today's money (buy) | — |
| In today's money (rent) | — |
| Break-even year | — |
| Worst 10% outcome (difference) | — |
| Median outcome (difference) | — |
| Best 10% outcome (difference) | — |
Two paths run side by side for every year:
Whoever ends with more wins, given your assumptions.
| Metric | What it tells you |
|---|---|
| Price-to-rent ratio | Home price divided by annual rent. Below 15 favours buying, above 20 favours renting. It is the fastest sanity check available. |
| Break-even year | The first year buying pulls ahead. If it is beyond the time you expect to stay, renting wins by default. |
| Monte Carlo probability | 1,000 runs with appreciation and returns varied randomly. A 52% result means the decision is a coin flip, not a strategy. |
A single deterministic answer hides how fragile it is. Change appreciation from 3% to 1% and the verdict flips; nobody knows future appreciation to that precision. The Monte Carlo runs the comparison 1,000 times, drawing appreciation and investment return from a normal distribution around your inputs, and reports how often buying came out ahead.
If the answer comes back at 50 to 60 percent, the two options are financially equivalent within the noise — decide on lifestyle, stability and flexibility instead. If it comes back above 75 percent, the maths genuinely favours one side.
$400,000 home, 20 percent down, 6.5 percent for 30 years, 1.1 percent tax, 1 percent maintenance, 3 percent appreciation, $2,000 rent growing 3 percent, 6 percent investment return, 10 years:
That margin is small enough that the Monte Carlo probability lands near 55 to 65 percent. Which is the honest answer: at these inputs, it is close.