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 $$1$ million. You have $$200,000$ 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 $$800,000$ mortgage, and is offering a standard $30-$year mortgage at

a $9\%$ 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, $$800,000$ loan at a

fixed nominal interest rate of $9\%($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?

$$1,096,664\mathrm{.}83$

$$1,182,341\mathrm{.}77$

$$856,769\mathrm{.}40$

$$1,010,987\mathrm{.}89$

Which of the following statements is not true about mortgages?

If the payment is less than the interest due, the ending balance of the loan will decrease.

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

Every payment made toward an amortized loan consists of two parts$-$interest and

repayment of principal.

Mortgages are examples of amortized loans.