A mortgage payment is not one number. Principal and interest depend on the price, your down payment, the rate, and how long you stretch the loan — and the last two move the total cost far more than the price does. Taxes and insurance are separate, and are not included here.
Principal and interest only. Taxes, insurance, and association fees are separate.
30-year term, fixed rate. The interest share climbs with the rate and the term.
Early payments are mostly interest, so the balance barely moves at first — that is amortization, not a bank trick. Because mortgage rates track long-term bond yields rather than the policy rate directly, a one-point difference on a loan this size changes the monthly payment by several hundred dollars over 30 years, which is why the rate you lock matters more than the price you negotiate.