Three years ago the Biggs purchased a house for $$675,000.$ They made a down payment of $20\%$ and took out a mortgage with BMO for the balance. They amortized the mortgage over $25$ years at $3\mathrm{.}2\%$ compounded semi$-$annually for a $3-$year term.

$($a$)$ Calculate their monthly payment. The bank rounds the payment up to the next dollar.

$($b$)$ How much of the $36$th payment was interest? Express your answer in $2$ decimal places and do not enter $"$$$"$ sign.

$($c$)$ How much interest did they pay in the $3$rd year $($Year $3)$ of the mortgage? Express your answer in $2$ decimal places and do not enter $"$$$"$ sign.

e$)$ After making three years of payments, they made a lump$-$sum payment to reduce the balance owing to $$460,000.$ How much was the lump$-$sum payment? Express your answer in $2$ decimal places and do not enter $"$$$"$ sign.