Assume that a lender offers a $30-$year, $$153,000$ adjustable rate mortgage $($ARM$)$ with the following terms:Based on estimated forward rates, the index to which the ARM Is tled is forecasted as follows: Beginning of year $($ BO h $2=7$ percent; $($BOY$)3=8\mathrm{.}5$ percent; $($BO $)4=9\mathrm{.}5$ percent; $($BO $)5=11$ percent.

Required:

a$.$ Compute the payments and loan balances for the ARM for the five$-$year period.

b$.$ Compute the yleld for the ARM for the five$-$year period.