An ARM is made for $$195,000$ for $30$ years with the following terms:

Initial interest rate $=7$ percent

Index $=1-$year Treasuries

Payments reset each year

Margin $=2$ percent

Interest rate cap$=$ None

Payment cap$=5$ percent increase in any year

Discount points $=2$ percent

Fully amortizing; however, negative amortization allowed if payment cap reached

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.