A floating rate mortgage loan is made for $$105,000$ for a $30-$year period at an initial rate of $12$ percent interest. However, the borrower and lender have negotiated a monthly payment of $$840.$

Required:

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

What will be the loan balance at the end of year $2?$ If the interest rate increases to $13$ percent at the end of year $2$ and the payment remains at $$840,$ how much is the total interest $($mortgage payment plus negative amortization$)$ in year $2$ and total interest $($mortgage payment plus negative amortization$)$ in years $2$ to $5?$