Laura and Martin obtain a $30-$year, $$100,000$ conventional mortgage at $10\mathrm{.}5\%$ on a house selling for $$130,000.$ Their monthly mortgage payment, including principal and interest, is $$915\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?

a$)$ The total amount that Laura and Martin will pay for their house is $

$($Round to the nearest dollar as needed.$)$