A professsional engineering is trying to purchase their first home. Consider a situation where $70\%$ of their $$75K$ annual salary is considered disposable income $($after taxes$/$health insurance and such$).$ In attempting to get pre$-$approval for a loan, the banker has indicated that $35\%$ is the maximum amount of their disposable income that can go towards the monthly mortgage payment. The quoted rate for a $30-$year mortgage is currently $6\mathrm{.}24\%($compounded monthly$)$ and the engineer has saved $$20K$ for the down payment. What is the maximum purchase price of a home they can afford? Careful use months for the time period.