A borrower has been analyzing different adjustable rate mortgage $($ARM$)$ alternatives for the purchase of a property. The

borrower anticipates owning the property for five years. The lender first offers a $$159,000,30-$year fully amortizing ARM

with the following terms:

Initial interest rate $=6$ percent

Index $=1-$year Treasuries

Payments reset each year

Margin $=2$ percent

Interest rate cap $=$ None

Payment cap $=$ None

Negative amortization $=$ Not allowed

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 unrestricted ARM for the five$-$year period.

b$.$ Compute the yield for the unrestricted ARM for the five$-$year period.