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5. (10\%) Seven years ago, Carlos took out a mortgage for $185,000 at 5.6 percent APR, compounded monthly, for 30 years. He has made all of the monthly payments as agreed. What is his current loan balance? 6. (10%) You are in the process of purchasing a new automobile that will cost you $25,000. The dealership is offering you either a $1,000 rebate (applied toward the purchase price) or 5.0% financing for 60 months (with payments made at the end of the month). This means that monthly interest rate is 0.05/12. You have been pre-approved for an auto loan through your local credit union at an interest rate of 6.5% for 60 months. This means that monthly interest rate is 0.065/12. Should you take the $1000 rebate and finance through your credit union or forgo the rebate and finance through the dealership at the lower 5.0% APR? 7. (10\%) A tall Starbucks coffee costs $5.00 a day. If the bank's quoted interest rate is 5% APR with daily compounding, and if the Starbucks price never changed, what would a lifetime free subscription to Starbucks coffee (a cup a day) be worth today, assuming you will live for 50 more years? What is the additional value of the subscription today that allows you to bequeath or sell it after 50 years (assuming that it gives a cup a day infinitely)