You and your spouse have found your dream home. The selling price is $220,000; you will put $50,000 down and obtain a 30-year fixed-rate mortgage at 12% compounded monthly for the balance. Assume that monthly payments begin in one month. What will each payment be? How much interest will you pay (in dollars) over the lifetime of the loan? (Assume you make each of the required 360 payments on time.) Although you will get a 30-year mortgage, you plan to prepay the loan by making an additional payment each month along with your regular payment. How much extra must you pay each month if you wish to pay off the loan in 20 years? Your banker suggests that, rather than obtaining a 30-year mortgage and paying it off early, you should simply obtain a 15-year loan for the same amount. The rate on this loan is 10% compounded monthly. By how much will your monthly payment be (higher/lower) for the 15-year loan than the regular payment on the 30-year loan?