Mortgages, loans taken to purchase a property, involve regular payments at fixed intervals and are treated as reverse annuities. Mortgages are the reverse of annuities, because you get a lump$-$sum amount as a loan in the beginning, and then you make monthly payments to the lender.

You$$ve decided to buy a house that is valued at $$1$ million. You have $$250,000$ to use as a down payment on the house, and want to take out a mortgage for the remainder of the purchase price. Your bank has approved your $$750,000$ mortgage, and is offering a standard $30-$year mortgage at a $10\%$ 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 in percentage form 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, $$750,000$ loan at a fixed nominal interest rate of $10\%($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 in percentage form 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?

$$918,259\mathrm{.}20$

$$1,267,197\mathrm{.}70$

$$1,175,371\mathrm{.}78$

$$1,083,545\mathrm{.}86$

Which of the following statements is not true about mortgages?

$1.$The payment allocated toward principal in an amortized loan is the residual balance$$that is$,$ the difference between total payment and the interest due.

$2.$Mortgages always have a fixed nominal interest rate.

$3.$The ending balance of an amortized loan contract will be zero.

$4.$Mortgages are examples of amortized loans.