Lucas just got a VRM $($variable rate mortgage$)$ of $500,000.$ he chooses to make

weekly payments. The first term is $5$ year. Assume the mortgage rate j$12=6\%(12$ is compounding

frequency$)$ when the mortgage contract was signed. Amortization period $=30$ years.

$($a$)$ Given the above interest rate, how much is the weekly PMT$?$

$($b$)$ At the start of the $2$nd year, suppose the rate becomes j$12=7\%.$ Lender wants to adjust the

weekly PMT$,$ asking Lucas to retire mortgage same pace as initially scheduled $($hint: how many years to go$?).$ How much would be new PMT$?$

$($c$)$ At the start of the $2$nd year, suppose the rate becomes j$12=5\%.$ Lender wants to adjust the weekly PMT$,$ asking Lucas to retire mortgage same pace as initially scheduled. How much would be new PMT$?$

Calculate it$!!!!$