You have just graduated from MSU, and have landed a job with a starting salary of $$75,000$ per year. You have decided to buy a house, and you have $$10,000$ saved up from your part$-$time job at Qdoba. The Eighth National Bank of DeWitt is offering to give you a $30-$year mortgage at $9\mathrm{.}7\%$ annual interest with monthly payments, but they will not give you a loan that will involve monthly payments of more than $25\%$ of your monthly income. Assuming you will borrow as much as you can from this bank, and assuming closing costs of $4\%,$ what is the highest price you will be able to pay for the house?