The Nicols are buying a house selling for $$435,000.$ They pay a down payment of $$35,000$ from the sale of their current house. To obtain a $15-$year mortgage at a $7\%$ interest rate, the Nicols must pay $1\mathrm{.}5$ points at the time of closing.

a$)$ What is the amount of the mortgage?

b$)$ What is the cost of the $1\mathrm{.}5$ points?

a$)$ The amount of the mortgage is $ $].$

b$)$ The cost of the $1\mathrm{.}5$ points on the mortgage is $ $$