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 Interest rate cap $=$ None Payment cap $=5$ percent increase in any year Fully amortizing; however, negative amortization is allowed if the payment cap is reached Based on estimated forward rates, the index to which the ARM is tied is forecasted as follows: Beginning of year $(BOY)3=8\mathrm{.}5$ percent; $(BOY)4=9\mathrm{.}5$ percent;

Compute the payments, loan balances,

$1-$ A $3/1$ ARM is made for $$150,000$ at $7$ percent with a

a$.$ Assuming that fixed payments are to be made semiannually for three years and that the loan is fully amortizing, what will be the semiannual payments?

b$.$ What will be the loan balance after three years?

c$.$ What would new payments be beginning in year $4$ if the interest rate fell to $5$ percent?