Consider a $15-$year fixed$-$rate mortgage for $$325000$ with a $3\mathrm{.}19\%$ APR.

$1.$ Prepare a loan amoritization schedule for the mortgage.

$2.$ What is the balance of the loan after $7$ years of payments?

$3.$ How many installments $($payments$)$ must be made before more than half of the payment amount is applied to the principal?