You have a $6-1$ ARM with a $30-$year loan term with an interest rate of $3\mathrm{.}2\%$ compounded monthly. Your monthly mortgage payments for the first seven years are $$2,300$ per month. For parts $($a$)$ and $($b$)$ use units and context in your answers, round to two decimal places.

a$)$ Calculate how much money you owe on the principal after seven years of payments.

b$)$ Your new interest rate is $4\mathrm{.}5\frac{\%}{?}$ year compounded monthly. What will your new monthly mortgage payment be$?$