An ARM is made for $$150,000$ 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 $=5$ 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.

You need to show your detailed calculation steps for every year, including what monthly payment you are using every year and why you are using it$.$ Tables are not allowed.

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.