Using the approximation formula for bond returns, and the modified duration of this annuity, calculate the approximate profit or loss that your firm would face if, right after issuing a credit card to the typical consumer, monthly interest rates increased to 1% a month, from the .8% they had been previously.

Using the approximation formula for bond returns, and the modified duration of this annuity, calculate the approximate profit or loss that your firm would face if, right after issuing a credit card to the typical consumer, monthly interest rates increased to 1% a month, from the .8% they had been previously. Instructions: Please answer a selection of the questions below. You must answer the questions found in Part I of this exam ("time value of money and bonds"). Then you may select either Part II or Part III. Please show your calculations and explain all answers. For the short answer questions, you should explain yourself as clearly as possible, but you do not need to be extremely detailed. 1-2 sentences should be fine. If you do not have enough room in the space provided to answer a given question, you are welcome to continue on the back of the page, or to use a separate sheet of paper. To emphasize: complete part I and then either part II or part III. Part I. Time Value of Money and Bonds You recently got a job working for a credit card company. You are working in the department that oversees some of the "rewards programs" associated with the credit cards your company offers. One of the simpler programs is a "cash back" rewards program. In this program, your company offers 4% cash back on purchases in certain categories (e.g. restaurants, entertainment, and groceries). The way this works is that if one of the holders of this credit card spends $100 on approved purchases in a given month, then at the end of the month, your company would pay that cardholder $4.00 ( 4% of the $100 spent during that month). To compensate for these rewards, you also charge cardholders an annual fee. A cardholder would pay this fee once at the beginning of the year, and then receive cash back at the end of each month. 1. Suppose that a typical consumer with this card will spend $2,000 in a month. You can assume then, that in a typical year this consumer will spend $2,000 each month for 12 months. Your corporate treasurer tells you that your company can earn . 8% interest per month investing the money that you receive when you collect cardholders' annual fees. Based on this return, what is the least that you could afford to charge cardholders as an annual fee in order to break even on your rewards program