$($a$)$ Using the house price you found in part $4,$ calculate the monthly mortgage payments based on a $30-$year mortgage, $7\%$ interest rate, and $5\%$ down payment. Round your answer to the nearest dollar. $($Hint: If you're using a calculator other than Desmos and the formulas we've been using in class, make sure you set the taxes$/$fees$,$ and any other extra information to $0$ before answering.$)$

$($b$)$ How much interest will you pay at the end of this mortgage? Round your answer to the nearest dollar.

$($c$)$ Repeating the process from $($a$),$ find the monthly mortgage payments based on a $15-$year mortgage instead. Round your answer to the nearest dollar.

$($d$)$ How much interest will you pay at the end of this mortgage? Round your answer to the nearest dollar.

$($e$)$ How much money do you save on interest by taking out a $15-$year loan instead of a $30-$year loan. Round your answer to the nearest dollar.

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$($Note: If you cannot afford a $15-$year loan, you can always make extra payments of any amount to pay down your principal and save on interest over the life of the loan. A small amount of principal early on in a $30-$year loan can save thousands of dollars over the life of the loan.$)$

The house price is $$442,500$