22. J&G Bank receives a large number of credit-card applications each month, an average of 30,000 with a standard deviation of 4,000, normally distributed. Approximately 60% of them are approved, but this typically varies between 50%

and 70%. Each customer charges a total of $2,000, normally distributed, with a standard deviation of $250, to his or her credit card each month. Approximately 85% pay off their balances in full, and the remaining incur finance charges.

The average finance charge has recently varied from 3% to 4% per month. The bank also receives income from fees charged for late payments and annual fees associated with the credit cards. This is a percentage of total monthly charges and has varied between 6.8% and 7.2%. It costs the bank $20 per application, whether it is approved or not. The monthly maintenance cost for credit-card customers is normally distributed with a mean of $10 and standard deviation of

$1.50. Finally, losses due to charge-offs of customers’ accounts range between 4.6% and 5.4% of total charges.

a. Using average values for all uncertain inputs, develop a spreadsheet model to calculate the bank’s total monthly profit.

b. Use Monte Carlo simulation to analyze the profitability of the credit card product. Use any of the Risk Solver Platform tools as appropriate to fully analyze your results and provide a complete and useful report to the manager of the credit card division.