> Does their mortgage balance increase too kind of like they took a loan out?
Yes. You are getting a new, larger mortgage, that will first pay off the previous mortgage and any extra will be paid directly to you. However, the new larger loan is equal to the price to pay off the mortgage plus the extra money.
The benefit is just like any other loan, that you get $30,000 now, instead of having to save $30,000 over a long period of time.
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