The Johnsons have accumulated a nest egg of $$50,000$ that they intend to use as a down payment toward the purchase of a new house. Because their present gross income has placed them in a relatively high tax bracket, they have decided to invest a minimum of $$2800/$month in monthly payments $($to take advantage of the tax deduction$)$ toward the purchase of their house. However, because of other financial obligations, their monthly payments should not exceed $$3100.$ If the Johnsons decide to secure a $15-$year mortgage, what is the price range of houses that they should consider when the local mortgage rate for this type of loan is $4\%/$year compounded monthly? $($Round your answers to the nearest cent.$)$

least expensive $

most expensive