PROBLEM $2(25$ MARKS$)$

After deciding to buy a new car, you can either lease the car or purchase it on a three$-$year loan. The car you wish to buy costs $$35,000.$ The dealer has a special leasing arrangement where you pay $$99$ today and $$499$ per month for the next three years. If you purchase the car, you will pay it off in monthly payments over the next three years at a $6$ percent Annual Percentage Rate $($the monthly rate is $6\frac{\%}{12}).$ You believe you will be able to sell the car for $$23,000$ in three years.

a$)$ What is the cost of buying the car? $(7$ marks$)$

b$)$ What is the cost of leasing the car? $(6$ marks$)$

c$)$ Should you buy or lease the car? $(6$ marks$)$

d$)$ What break$-$even resale price in three years would make you indifferent between buying and leasing? $(6$ marks$)$