The Johnsons have accumulated a nest egg of $$40,000$ that they intend to use as a down payment toward the purchase of a new house. Because their present gross income has placed them in a relatively high tax bracket, they have decided to invest a minimum of $$2400/$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 $$3000.$ If local mortgage rates are $5\mathrm{.}5\%/$year compounded monthly for a conventional $30-$yr mortgage, what is the price range of houses they should consider?