Consider a consumer who lives three periods and is currently at period t=1. He earns a fixed income of $2500 every period. At period 1, he decides to take a loan of $1500 from his credit card to buy a TV at period t=1.

In period t=2, the consumer decides how he is going to pay back the loan. The credit card company gives two payment options. The first option is to pay the amount full in period 2. If this option is chosen, the consumer does not need to pay any interest. The second option is to pay half of the amount ($750) in period 2 without any interest, and the other half ($750) in period 3 with an interest of r (0

The consumer's immediate utility at each period equals to the amount of dollars he holds. For example, if the consumer takes the first payment option, at t=1, his immediate utility is the fixed income of $2500 plus $ 1500 that he borrows from the credit card company. Likewise, at t=2, his immediate utility is the fixed income of $2500 minus $1500 that he pays back to the credit company. Thus, his immediate utility at each period, under each payment option, can be summarized as follows.

\f