The Clarke family is buying a home and will select a mortgage with a $25-$year amortization period, at a rate of $6\%$ compounded semiannually for a $5-$year term. The monthly mortgage payment will be their only debt payment. The family's gross monthly income is $$8,400.$ Property taxes are estimated at $$500$ per month, and heating costs at $$375$ per month. The bank has upper limits of $39\%$ for GDS and $44\%$ for TDS$.$ What is the maximum mortgage for which the Clarkes qualify? $($Round your final answer to the nearest dollar.$)$Maximum mortgage$$01$:$13$:$33$