14 PROBLEMS MATHEMATICS AND STATISTICS FOR FINANCIAL RISK MANAGEMENT 1. Solve for y, where: a. y = ln(e5) b. y = ln(1/e) c. y = ln(10e) 2. The nominal monthly rate for a loan is quoted at 5%. What is the equivalent annual rate? Semiannual rate? Continuous rate? 3. Over the course of a year, the log return on a stock market index is 11.2%. The starting value of the index is 100. What is the value at the end of the year? 4. You have a portfolio of 10 bonds. In how many different ways can exactly two bonds default? Assume the order in which the bonds default is unimportant.