Carville Chrysler offers a special deal of leasing Dodge RAM 1500 pickup trucks. With a lease, the purchaser has the option of buying the vehicle at the end of the lease. For example, suppose a $27,357 vehicle could be leased with a certain monthly payment for 36 months, and then the customer has the option to buy it for $10,669.23, where the amount $10,669.23 is called the residual value, which is set to 39% of the purchasing price of $27,357. The monthly payment is related to the purchase price as well as the residual value, and the purchase price is set at the time when the vehicle is leased. Now Carville needs to decide on their leasing strategy.

(a) At 6.7% interest compounded monthly, what should Carville charge as a lease payment to ensure that they recover their expenses (assuming the customer buys the car at the end of the lease). Lease payments are made at the start of each month.

(b) To encourage customers to lease vehicles, Carville may consider reducing the lease payments down to $529.99, by using a higher residual value in the calculation. What residual value is used in the calculation for the lease payment of $529.99?

(c) Although Carville may increase short-term sales by reduced monthly payment, but they may have trouble to sell the vehicle at the end of 36 months if the residual value is high. With a higher residual value, the customer is less likely to buy the vehicle at the end of the lease. To offer a lower residual value, however, the company may lose money on the vehicle leased. Suppose Carville offers a promotion deal on the vehicle with monthly payment of $529.99 and residual value of $10,669.23. Determine the corresponding purchase price. With this promotion strategy, how much will the company loss on each vehicle leased in terms of purchase price?