$4.$ Mortgage payments

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 $$1$ million. You have $$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

$10\%$ 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 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 $10\%($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 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?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 $10\%($APR$),$ then the difference in the monthly payment of the $15-$year

mortgage and $30-$year mortgage will be $$1,773\mathrm{.}35vv?($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?

$$1,521,333\mathrm{.}25$

$$1,411,091\mathrm{.}71$

$$1,102,415\mathrm{.}40$

$$1,300,850\mathrm{.}17$

Which of the following statements is not true about mortgages?

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

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

the interest due.

Mortgages always have a fixed nominal interest rate.

Mortgages are examples of amortized loans.