Let$$s say you are buying a home, putting $15\%$ down and financing the rest with a $30-$year mortgage. The price of the home you are buying is $$1,000,000$ and the APR is $6\mathrm{.}85\%.$

$1.$ Determine your monthly payment amount.

$2.$ Assuming you pay only the monthly payment each month, how much will you pay in total over the life of the loan?

$3.$ Assuming you paid only the monthly payment each month as in question $2,$ how much of your total paid will have been interest?

$4.$ How much of your $12$th payment will go towards the principal of the loan?

$5.$ What is the remaining principal on your loan at $15$ years?