A family has a $$$$99,756,25-$year mortgage at $7\mathrm{.}5\%$ compounded monthly.

$($A$)$

Find the monthly payment and the total interest paid.

$($B$)$

Suppose the family decides to add an extra$$ $$100$ to its mortgage payment each month starting with the very first payment. How long will it take the family to pay off the$$ mortgage? How much interest will the family$$ save?