Assume you work for a company that leases automobiles. An auto dealership contacts you and tells you that it has a customer that wants to lease a car and can arrange for your company to purchase the vehicle and then lease it to the customer. Note that an important variable for you as a leasing firm is the residual value of the vehicle when the lease matures and you as the leasing firm must sell the vehicle. It must be forecast and as a result is the source of much of the risk in the lease. The customer that they have has sufficient credit and wants to lease a $42,000 vehicle for 4 years with monthly payments. Your competitor is a leasing company that offers leases for the vehicle requiring the customer to have a down payment of $4,000 and monthly lease payments of $575 beginning when the lease is signed. So at the signing the customer must pay $4,575. If your firm meets the competitors' terms, what must the residual value be at the end of the lease in 4 years for your firm to earn 9% on the lease? Assume the customer will not exceed the mileage restriction and there is no damage to the vehicle. Note that the residual value is as of the date the vehicle is returned to the leasing firm, which is one month after the final payment (the 48th month). It assumes the vehicle will be sold immediately, which might not be realistic but is the easiest assumption. Assume monthly compounding for all calculations.