Real Estate Law
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Typically, in a refinance situation, the lender looks at the fair market value of the property versus the amount of the loan in order to establish the percentage of equity. Different lenders require different amounts of equity. The problem that I think you might have will be in having a trust as the co-borrower and owner. I suspect that they will want you to be the borrower initially and then you can partially deed the property into the trust later. You will have to call a number of mortgage brokers to find out if, and how that can be done.
Then the trustee will have to qualify for the loan too.