Rome Corporation is concerned that customers are not trading in their uPhones as frequently as Rome would like. Currently, the average customer holds onto a uPhone for thirty$-$six months before trading in their current phone and purchasing a new one. Rome has a plan to encourage customers to trade$-$in their uPhones every twenty$-$four months. A uPhone trade$-$in is expected to provide a contribution margin of $$200$ per phone indefinitely. Under the new plan, trade$-$ins of uPhones would not only occur every twenty$-$four months, but would grow at an annual rate of $2\%.$