An SUV sells for $$34200$ and can be leased for $$348\mathrm{.}00$ per month plus taxes for a $48-$month lease. A down payment of $$3500$ is required and the residual value of the SUV at the end of the lease is $$16495\mathrm{.}00.$ At the end of the lease, the vehicle will be purchased for the residual value plus taxes. This amount will be financed for three years at $4\%.$

a$)$ Calculate the total cost of the lease.

b$)$ Calculate the total cost to finance the residual value of the vehicle.

c$)$ What is the total amount paid to lease and then purchase the SUV?