$3.$ You usually go to the theater to see a lot of movies. Now you are considering a new streaming service that requires proprietary DVR and streaming movies instead. You currently pay $$9$ per movie when you go to the theater but if you buy the DVR you will have to pay only $$5$ per movie rental. You estimate that the DVR will cost $$400($at t $=0)$ and will last $3$ years. Except for cost, you are indifferent to seeing movies at home or in the theater. Assume that the cost of theater tickets and rental payments occur at the end of each month and that you use the DVR only to watch movies. Assume that you watch the same number of movies every month. Your discount rate is $1\%$ per month. Assume that there is no inflation. How many movies per month must you watch for the DVR purchase to be a smart purchase?