As a loan officer for a bank, you are meeting with a customer who ears $$85,280$ per year after deductions. This customer would like to purchase a $$350,000$ house and will be able to make a down payment of $10\%.$ Your institution is offering mortgages at $6\mathrm{.}2\%,$ compounded semi$-$annually, for $20$ years. A condition for granting the loan is the mortgage payments cannot exceed one$-$third of the customer's monthly salary. Does this customer qualify for a loan and, if not, what recommendations would you make? Show all your calculations. $[/8]$