Jimmy pays a $200 annual fee at a fitness center rather than paying the $2 charge that it would cost if he paid by the visit. He intends to go 100 times in the year. He claims that the fee will act as a commitment device to help him follow his wish to exercise regularly and the per-visit fee would not act as a commitment device. His friend tells him that the cost is $100 either way so his reasoning is false. Do you agree that the annual fee can act as a commitment device for Jimmy and the per-visit fee would not? Explain your answer. (Assume a zero interest rate so the timing of payments is not affected by foregone interest.)