A young married couple has carefully looked at their budget. After review, they can afford a monthly mortgage payment of $$1,105\mathrm{.}85.$ They go to their local banker and she offers them a mortgage of $5\mathrm{.}04\%$ APR with monthly compounding with a term of $30$ years. The couple has enough savings to pay $20\%$ down, so the mortgage will be $80\%$ of the home$$s value.

With this mortgage and a $20\%$ down payment, what priced house can the couple afford?