You are thinking of buying a used car for $4,000 for driving to school. Your parents are willing to lend you the $4,000 and charge only 2.4% APR. They want the loan repaid equally in 48 monthly payments, with the first payment due at the end of the month in which you buy the car. You estimate that the monthly cost of operating the car, including gas, insurance, maintenance, and licence fees, will be $200 and payable at the start of each month. The cost of a monthly bus pass is $80. You expect that the car will be totally worn out in four years, with zero resale value, when you are finished school. Your discount rate is 6%, compounded annually.
a. If you have 3 roommates who also need transportation to and from school, how much do you need to charge each of them a month in order to cover all your costs? (You all plan to go to summer school, so you can assume 12 payments a year.)
b. Does it make financial sense to buy the car? Explain your answer.