A basic ARM is made for $$217,000$ 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:

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

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

c$.$ 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 $2?$

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

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