You are considering purchasing a new home. You will need to borrow $$350,000$ to purchase the home. A mortgage company offers you a $15-$year fixed$-$rate mortgage $(180$ month$)$ at $8\%$ APR. After having paid on this mortgage for $8$ years, you decide to sell your home. The sale price is expected to be $$450,000.$ How much net cash will you receive once you pay off the remainder of the mortgage?