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 500,000 to use as a down payment on the house, and you take out a mortgage for the rest. Your bank has approved your mortgage for the balance amount of $500,000 and is offering you a standard 30-year mortgage with 8% fixed nominal interest rate (called the annual percentage rate, or APR). According to this proposal, what will be your monthly mortgage payment? (Note: Round the final value of any interest rate used to four decimal places.) O $3,668.96 O $5,686.89 O $4,953.10 $4,586.20 Your friends suggest that you take a 15-year mortgage, because a 30-year mortgage is too long, and you will lose a lot of money on interest. If your bank approves a 15-year, $500,000 loan at a fixed nominal interest rate of 8% (APR), what will be the difference in the monthly payment of the 15-year mortgage and 30-year mortgage? (Note: Round the final value of any interest rate used to four decimal places.) $1,275.83 O $1,109.42 O $1,830.54 O $1,608.66