You can purchase a battery system for $6,500 that can store 13.5kWh of energy. The average price of electrical energy is around $0.13 per kWh. Assume the power company would charge a high rate for part of the day(when there is a peak in demand), and a low (off peak) rate for the rest of the day. Also assume that the power company is willing to buy the power back from you and that your battery system is 95% efficient. For simplicity assume there is only one peak period every day and that the average of the two rates is still $0.13 kWh.

a. If the peak rate were fifty percent higher than the off-peak rate, how long would it take to pay off the battery system?

b. What is the largest possible difference between the rates and use it to find the fastest possible payoff period?