There are two common choices for the term of a home mortgage: $15$ or $30$ years. Suppose you need to borrow $80,000$ at an APR of $6\mathrm{.}6\%$ to buy a home.a$.$ What will your monthly payment be if you opt for a $15-$year mortgage?b$.$ What percentage of your first months payment will be interest if you opt for a $15-$year mortgage?c$.$ How much interest will you have paid by the end of the $15-$year loan?d$.$ What will your monthly payment be if you opt for a $30-$year mortgage?e$.$ What percentage of your first months payment will be interest if you opt for a $30-$year mortgage?f$.$ How much interest will you have paid by the end of the $30-$year loan? Is it twice as much as for a $15-$year mortgage?