Problem II:

Suzan Long is considering buying a home for $$350,000.$

$($a$)$ If she makes a down payment of $$50,000$ and takes out a mortgage on the rest of the money at $5\mathrm{.}5\%$ compounded monthly, what will be her monthly payment to retire the mortgage in $15$ years?

$($b$)$ Consider the $60$th payment. How much will the interest and principal payments be$?$

$($c$)$ After completing her ${60}^{th}$ payment, how much will she still have to pay from the borrowed principle?