Jake has successfully bid for a house at $600,000.$ Assume the lending value assessed by the lender is of the same size as the purchase price. He has saved a down payment of $100,000.$

$($a$)$What type of mortgage he would have: conventional or high$-$ratio?

$($b$)$ Given your answer of $($a$),$ would he have to buy mortgage default insurance? If so$,$ how much? Use the following chart on mortgage insurance fee $($MIF$).$

$\backslash$table$[[$Down Pay $\%,$LVR$\%,$MIF$],[15-19\mathrm{.}99\%,80\mathrm{.}01-85\%,2\mathrm{.}80\%$