A car costs $$13,400.$ Alternatively, the car can be leased for $3$ years by making payments of $$291$ at the beginning of each month and then bought at the end of the lease for $$4,865.$ If interest is $12\%$ compounded quarterly,a$)$ How much would it cost to buy the car immediately?b$)$ How much would it cost to lease first and then buy it$?$c$)$ Which alternative is preferable?