You plan to buy a house that sells for $$250,000.$ You plan to put $10\%$ down and finance the rest. You are exploring the following financing options:

i$.30-$yr mortgage with a stated annual interest of $6\mathrm{.}5\%$

ii$.15-$yr mortgage with a stated annual interest of $6\%.$

You plan to pay off the loan by making equal monthly payments.

a$.$ What would be your monthly payment if you take the $30-$yr mortgage? How much $($total$)$ interest would you pay over the life of the loan? $$1422\mathrm{.}15,$$$286,974$

b$.$ What would be your monthly payment if you take the $15-$yr mortgage? How much $($total$)$ interest would you pay over the life of the loan? $$1898\mathrm{.}68,$$$116,762\mathrm{.}01$