What PMI is and what it costs
Private mortgage insurance protects the lender (not you) for low-down-payment loans — typically 0.3–1.2% of the loan per year, i.e. $90–360/month on a $357k loan. On conventional loans it is cancellable; on many government loans the equivalent (MIP) is not, which changes the whole comparison.
When it ends automatically
By law, PMI on conventional loans auto-terminates at 78% of the original value (scheduled mid-2020s for typical loans), and you may request cancellation at 80% — earlier if appreciation or improvements pushed your equity there. The lender will not chase you; the request, with an appraisal if needed, is on you.
Killing it sooner
Three levers: extra principal (the extra-payment calculator shows when you cross 80%), a value-based reappraisal after a strong local market or real improvements, and — for new buyers — pricing whether 20% down beats PMI plus earlier entry. Often PMI plus buying two years earlier beats saving for the full 20% — run both paths with real numbers, not folklore.