Assume that a lender offers a $30-$year, $$142,000$ adjustable rate mortgage $($ARM$)$ with the following terms: Initial interest rate $=7\mathrm{.}5$ percentIndex $=$ one$-$year TreasuriesPayments reset each yearMargin $=2$ percentInterest rate cap $=1$ percent annually; $3$ percent lifetimeDiscount points $=2$ percentBased on estimated forward rates, the index to which the ARM is tied is forecasted as follows: Beginning of year $($BOY$)2=7$ percent; $($BOY$)3=8\mathrm{.}5$ percent; $($BOY$)4=9\mathrm{.}5$ percent; $($BOY$)5=11$ percent. Required:a$.$ Compute the payments and loan balances for the ARM for the five$-$year period.b$.$ Compute the yield for the ARM for the five$-$year period.