Adjustable$-$rate Mortgage Assume the following for an adjustable rate

mortgage loan that is tied to the one$-$year Treasury rate$(6$ points$)$:

Loan amount: $$150,000$

Annual rate cap: $2\%$

Life$-$of$-$loan cap: $5\%$

Margin : $2\mathrm{.}75\%$

First$-$year contract rate: $5\mathrm{.}50\%$

One$-$year Treasury rate at end of year $1$: $5\mathrm{.}25\%$

One$-$year Treasury rate at end of year $2$: $5\mathrm{.}50\%$

Loan term in years: $30$

$($a$)$ What is the initial monthly payment?

$($b$)$ What is the loan balance at the end of year $1?$

$($c$)$ What is year $2$ contract rate?