You plan to purchase a house for $$190,000$ using a $30-$year mortgage obtained from your local bank. You will make a down payment of $10$ percent of the purchase price. You will not pay off the mortgage early. Assume the homeowner will remain in the house for the full term and ignore taxes in your analysis.

a$.$ Your bank offers you the following two options for payment. Which option should you choose? $1.$ mortgage rate of $5\mathrm{.}80$ percent and zero points $2.$ mortgage rate of $5\mathrm{.}55$ percent and $1\mathrm{.}5$ points

b$.$ Your bank offers you options one mortgage rate of $5\mathrm{.}55$ percent and $1\mathrm{.}0$ point $2.$ mortgage rate of $5\mathrm{.}45$ percent and $2\mathrm{.}0$ points