Rework the previous problem for a case in which the 1-year warranty requires you to pay for the new device even if failure occurs during the warranty period.

Specifically, if the device fails at time t, measured relative to the time it went into use, you must pay $100t for a new device. For example, if the device goes into use at the beginning of April and fails 9 months later, at the beginning of January, you must pay $75. The reasoning is that you got 9/12 of the warranty period for use, so you should pay that fraction of the total cost for the next device. As before, however, if the device fails outside the warranty period, you must pay the full $100 cost for a new device.