Assume that a lender offers a $30-$year, $$157,000$ adjustable rate mortgage $($ARM$)$ with the following terms:

Initial interest rate $=7\mathrm{.}5$ percent

Index $=$ one$-$year Treasuries

Payments reset each year

Margin $=2$ percent

Interest rate cap $=1$ percent annually; $3$ percent lifetime

Discount points $=2$ percent

Based 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.