Mary earns $$58,000$ per year and her husband Joe earns $$60,000$ per year gross. They have debt as follows: a car loan with $$550$ per month payment, a visa which requires a minimum monthly payment of $$100,$ and combined student loan payments totaling $$350$ per month. The bank allows a $32\%$ GDS and $40\%$ TDS$.$ The house they wish to purchase has been appraised at $$410,000,$ however the purchase price is $$425,000$ because it is a seller's market. Monthly property taxes and heating costs are $$700$ per month total. They are applying for a conventional mortgage $($using $80\%$ maximum as the bank's rule$)$ and their selected term is at $3\%$ interest lender posted rate and the amortization is $25$ years. Currently, consider the Bank of Canada benchmark rate to be $5\mathrm{.}25\%$ for stress test purposes on conventional mortgages. Which of the following is closes to the maximum amount of a mortgage loan that Mary and Joe qualify for, based on the Total Debt Service $($TDS$)?$ a$.$ $$420,675$ b$.$ $$397,524$ c$.$ $$450,000$ d$.$ $$410,571$