What is the term for obtaining a new mortgage loan on a property already owned while paying off the existing loan?

The term for obtaining a new mortgage loan on a property already owned while paying off the existing loan is referred to as refinancing. This process involves taking out a new loan, typically at a lower interest rate or with different terms, which is then used to pay off the existing mortgage. Homeowners often refinance to reduce their monthly payments, shorten the loan term, or switch from an adjustable-rate mortgage to a fixed-rate mortgage.

In refinancing, the homeowner effectively replaces their old loan with a new one, which can provide financial relief and help in better managing the homeowner's finances. Refinancing also allows borrowers to access equity in their home if desired.

The other options represent different financial concepts: a reverse mortgage is a financial product for seniors that converts part of the equity in their home into cash; a home equity loan allows homeowners to borrow against the equity they have built up in their property but does not involve paying off an existing mortgage; a second mortgage refers to an additional loan taken out on a property that already has a primary mortgage, but it does not serve the purpose of paying off the first mortgage. Therefore, refinancing is the most accurate term for the action described in the question.