6. Assume you work for a company that leases automobiles. An auto dealership with a customer arranges for your employer to purchase the vehicle and then lease it to the customer. An important variable for the leasing rm is the "residual value\" of the vehicle when the lease matures and the leasing rm sells the vehicle. It must be forecast and as a result is the source of much of the risk in the lease. A customer with sufcient credit wants to lease a $42,000 vehicle for 4 years with monthly payments. Other leasing companies offer 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. The dealership has a good relationship with your rm and wants it to provide the lease but it must be competitive. If your rm meets the competitors' terms, what must the residual value be at the end of the lease in 4 years for your rm 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 rm, which is one month after the nal payment. Assume monthly compounding for all calculations