Consider a $$225,0005-1$ ARM amortized over $30$ years with monthly payments. The

loan is indexed to the $1-$year constant maturity Treasury security with a $3$ percent

margin and $2-6$ caps $(2$ percent annually and $6$ percent lifetime. The initial interest

rate on this loan is $4\mathrm{.}5$ percent.

a$)$ What is the initial monthly payment on this loan?

b$)$ How much will the borrower still owe on this loan at the first adjustment date $($the

end of the $5$th year$)?$

c$)$ Suppose that the yield on the $1-$year T$-$Bill is $3\mathrm{.}5$ percent at the first adjustment

date. What will the next payment be on the loan after it adjusts?

d$)$ If the yield on the $1-$year T$-$Bill is $2\mathrm{.}75\%$ at the next adjustment date, what will be

the new payment on the loan at that time?

e$)$ Suppose that the borrower must pay two points in conjunction with this loan and

expects to hold it for seven years. What is the loan$$s effective borrowing cost

$($EBC$)?$