A floating rate mortgage loan is made for $$135,000$ for a $30-$year period at an initial rate of $12$ percent interest. However, the borrower and lender have negotiated a monthly payment of $$1,080.$

Required:

a$.$ What will be the loan balance at the end of year $1?$

b$.$ If the interest rate increases to $13$ percent at the end of year $2,$ how much is the payment plus negative amortization in year $2$ and year $5$ if the payment remains at $$1,080?$