A person purchased a house $14$ years ago for $$225,000.$ The house was financed by paying $20\%$ down and signing a $30-$year mortgage at $8\mathrm{.}15\%$ on the unpaid balance. Equal monthly payments were made to amortize the loan over a $30-$year period. The owner now wishes to refinance the house because of a need for additional cash. The new appraised value of the house is $$310,000.$ If the loan company agrees to a new $30-$year mortgage of $85\%$ of the new appraised value of the house, how much cash will the owner receive after repaying the balance of the original mortgage?