The statement that correctly describes how a fixed-rate mortgage works is:
The monthly payment on a fixed-rate mortgage never changes.
In a fixed-rate mortgage, the interest rate is set for the entire term of the loan, which means that the monthly payment remains constant throughout the life of the loan, making it easier to budget.
The other statements about property taxes and the purchase price of the house are not accurate in the context of a fixed-rate mortgage. Property taxes can increase over time, and the purchase price of the house can change based on market conditions. Additionally, in a standard amortization schedule, part of the monthly payment goes towards interest and part towards the principal, so interest is not paid off entirely before the principal decreases.