Shakeia Duncan wants to know what home price she can afford. Her annual gross income is $$46,200.$ She owes $$840$ per month on other debts and expects her property taxes and homeowner's insurance to cost $$160$ per month. She knows she can get an $10\mathrm{.}50$ percent, $30-$year mortgage so her mortgage payment factor is $9\mathrm{.}15.$ She expects to make a $15$ percent down payment. What is Shakeia's affordable home purchase price?