You have just negotiated a $5-$year mortgage on $$332,100$ amortized over $25$ years at a rate of $4\mathrm{.}99\%$ per year compounded semiannually. a$)$ What are the monthly payments?  b$)$ What are the principal and interest payments each month for the first two months?  c$)$ What is the outstanding principal at the end of the first $5$ years?d$)$ Assume that at the end of the $5-$year contract your remaining outstanding principal is $$250,000.$ The interest rate on your mortgage is still $4\mathrm{.}99\%$ per year compounded semiannually, but you decide to switch to weekly payments $(52$ weeks per year$).$ What is the amount of your weekly payment? e$)$ Now say your mortgage contract allows you to make a larger weekly payment, and you choose to pay $$400$ per week. How many years will it take to pay off the rest of your mortgage? $($All other information is the same as part d$).$

$($Note: Please give comprehensive calculations and explanations$)$