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PROBLEMS

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. How many different ways can exactly two bonds default? Assume the order in which the bonds default is unimportant.

5. What is the present value of a perpetuity that pays $100 per year? Use an annual discount rate of 4%, and assume the first payment will be made in exactly one year.

6. ABC stock will pay a $1 dividend in one year. Assume the dividend will continue to be paid annually forever and the dividend payments will increase in size at a rate of 5%. Value this stream of dividends using a 6% annual discount rate.