You have just made an offer on a new home and are seeking a mortgage. You need to borrow $$$$582,000.$

a$.$ The bank offers a $25-$year mortgage with fixed monthly payments and an interest rate of $0\mathrm{.}55\%$ per month. What is the amount of your monthly payment if you take this$$ loan?

b$.$ Suppose you take the $25-$year mortgage described in part $($a$).$ How much will you still owe on the mortgage after $10$years$?$