A couple wants to purchase a new house and feel that they can afford a mortgage payment of $$700$ a month. They are able to obtain a $30-$year $7\mathrm{.}4\%$ mortgage $($compounded monthly$)$ but must put down $20\%$ of the cost of the house. Assuming that they have enough savings for the down payment, how expensive a house can they afford?

The couple can afford a house that costs up to $

$($Round the final answer to the nearest dollar as needed. Round all intermediate values to six decimal places as needed.$)$