You are considering leasing a car. After exhaustive negotiations, you have settled on a price for the car of $30,000 plus sales tax of 5.5%. Now comes the fun part. You have to decide whether to lease the car or purchase the car. If you buy the car you plan to use $30,000 that you would otherwise invest in a 3-year U.S. Treasury security that has an APR of 4.15% with semiannual compounding. The lease you are considering is zero money down (i.e. no down payment) and lasts for 36 months. If you lease the car you will make 36 monthly payments of $449.38 (including tax) with the option to buy the car for $18,000 (plus tax) at the end of the lease (i.e. in 3 years). a) Should you lease or purchase the car, if you plan to keep the car forever? b) Should you lease or purchase the car, if you plan to keep the car for only 3 years? (Assume you can sell the car for $18,000 in 3 years)