How Mortgage Time Machine calculates

Money, rates, and rounding

Money is integer cents, rates are integer millionths, and monthly growth factors are integer fixed point. Interest uses explicit half-up rational rounding. Scheduled payments are found by bounded integer search against the exact same ledger recurrence. No balance or crossover equality depends on binary floating-point cents.

Monthly event order

1. Open the month with the prior balance.
2. Apply scheduled interest and principal, then bounded extra principal.
3. Apply taxes, insurance, PMI, HOA, maintenance reserve, rent, and other displayed costs.
4. Grow the explicit home, rent, portfolio, cost, and inflation paths.
5. Apply refinance events after the named payment boundary.
6. Calculate gross equity, modeled selling costs, liquidation equity, and net worth.

Payment and amortization

The note rate—not APR—drives a conventional fixed-rate monthly payment. Zero-rate loans divide principal across the term. The final payment is capped at the remaining balance. Extra-payment rules never create a negative balance; unused excess is retained in the audit result.

Ownership, rent, and opportunity cost

Principal transfers cash into equity and is not counted as an unrecoverable cost. Interest, tax, insurance, PMI, HOA, maintenance reserve, and transaction costs are unrecoverable. Both paths start from common liquid assets and invest or withdraw the difference between a common housing budget and actual modeled outflow, preventing opportunity cost from being counted twice.

Sale, comparison, and crossover

Hypothetical liquidation equity equals modeled home value minus mortgage balance, proportional selling costs, and fixed selling costs. Comparisons use the same calendar month. First crossover is the first nonnegative month; stable crossover must remain nonnegative for six consecutive months.

Refinance

The old loan pays through the selected boundary. The replacement principal includes displayed financed costs and principal reduction. The result reports old/new payments, nominal cash break-even, discounted NPV break-even, remaining balances, horizon value, and term extension together.

Versions and limits

Engine: mortgage-engine/1.0.0. Methodology: mortgage-methodology/1.0.0. This is a monthly educational model. It is not a lender quote, APR disclosure, Loan Estimate, appraisal, parcel tax model, insurance quote, investment forecast, tax advice, or legal advice.