You are buying a new Audi A6. You have two options. The first option is you can buy the car outright for 72 monthly payments of $1,024 starting a month from today. Alternatively, you can first lease the car for 3 years and then buy the car at the end of the three year lease. The cost of the lease is $5,335 today and then 36 monthly payments, starting one month from today, of $769 a month. Finally, at the end of the last payment, you need to pay $34,655 for the car. The discount rate is 4.2% annual with monthly compounding.

a) Assuming the maintaining costs and insurance expense on the car is the same whether you buy or lease the car, should you buy the car outright or first lease the car for 3 years? (Need numerical proof for a correct answer)

b) Suppose that leasing a car will results in a higher insurance premium than owning a car, and the premium is payable at the end of each year during the 3 year leasing period. If you are indifferent between buying and leasing, what must be the difference in the annual insurance premium between the two options?