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 $$1$ million. You have $$350,000$ 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 $$650,000$ 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.$)$

uggest 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

s a $15-$year, $$650,000$ ioan at a fixed nominal interest rate of $10\%($APR$),$ then the difference in the monthly payment of the $15-$year

$30-$year mortgage will be

$.($Note: Round the final value of any interest rate in percentage form to four decimal places.$)$

t 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