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A basic ARM is made for $$205,000$ at an initial interest rate of $6$ percent for $30$ years with an annual reset date. The borrower believes that the interest rate at the beginning of year $($BOY$)2$ will increase to $7$ percent.

Required:

Assuming that a fully amortizing loan is made, what will the monthly payments be during year $1?$

Based on $($a$)$ what will the loan balance be at the end of year $($EOY$)1?$

Given that the interest rate is expected to be $7$ percent at the beginning of year $2,$ what will the monthly payments be during year $2?$

What will be the loan balance at the EOY $2?$

What would be the monthly payments in year $1$ if they are to be interest only?