Laura and Martin obtain a $25-$year, $$$$150,000$ conventional mortgage at $9\mathrm{.}5\%$ on a house selling for $$$$190,000.$ Their monthly mortgage$$ payment, including principal and$$ interest, is $$$$1311\mathrm{.}00.$

$$a$)$ Determine the total amount they will pay for their house.

$$b$)$ How much of the cost will be$$ interest?

$$c$)$ How much of the first payment on the mortgage is applied to the$$ principal?