It doesn't matter how much you pay to build the property. It matters what the property is worth. They will go off the appraisal and give you a mortgage based on a percentage of that amount.
Once you arrive apply for the mortgage the bank will do an appraisal. They will give you a mortgage up to 75% of the appraisal amount. My best guess is it should be pretty close to the $250k so the mortgage will be at most $188k.