You've decided to buy a house that is valued at $$1$ million. You have $$100,000$ to use as a down payment on the house, and want to take out a mortgage for the remainder of the purchase price. Your bank has approved your $$900,000$ mortgage, and is offering a standard $30-$year mortgage at a $12\%$ fixed nominal interest rate $($called the loan's annual percentage rate or APR$).$ Under this loan proposal, your mortgage payment will be per month. $($Note: Round the final value of any interest rate used to four decimal places.$)$

Your friends suggest that you take a $15-$year mortgage, because a $30-$year mortgage is too long and you will pay a lot of money on interest. If your bank approves a $15-$year, $$900,000$ loan at a fixed nominal interest rate of $12\%($APR$),$ then the difference in the monthly payment of the $15-$year mortgage and $30-$year mortgage will be $?($Note: Round the final value of any interest rate used to four decimal places. $)$

It is likely that you won't like the prospect of paying more money each month, but if you do take out a $15-$year mortgage, you will make far fewer payments and will pay a lot less in interest. How much more total interest will you pay over the life of the loan if you take out a $30-$year mortgage instead of a $15-$year mortgage?

$$1,388,431\mathrm{.}80$

$$1,638,349\mathrm{.}52$

$$1,777,192\mathrm{.}70$

$$1,916,035\mathrm{.}88$

Which of the following statements is not true about mortgages?

Mortgages are examples of amortized loans.

The ending balance of an amortized loan contract will be zero.

Mortgages always have a fixed nominal interest rate.

The payment allocated toward principal in an amortized loan is the residual balance$-$that is$,$ the difference between total payment and the interest due.