To make sure that Janet has the skills to do the job, Tom plans to give her a short test. As far as Tom is concerned, the single most important concept in financial planning, whether it be personal or corporate, is discounted cash flow (DCF) analysis. He believes that if Janet has solid skills in this area, then she will be able to succeed in her expanded role with minimal supervision. The basis for the test is an actual analysis that Tom is currently working on for one of his clients. The client has $10,000 to invest with a goal of accumulating enough money in 5 years to pay for his daughters first year of college at a prestigious Ivy League school. He has directed Tom to evaluate only fixed interest securities (bonds, bank certificates of deposit, and the like) since he does not want to put his daughters future at risk. One alternative is to invest the $10,000 in a bank certificate of deposit (CD) currently paying about 10 percent interest. CDs are available in maturities from 6 months to 10 years, and interest can be handled in one of two waysthe buyer can receive interest payments every 6 months or reinvest the interest in the CD. In the latter case, the buyer receives no interest during the life of the CD, but receives the accumulated interest plus principal amount at maturity. Since the goal is to accumulate funds over 5 years, all interest earned would be reinvested. However, Tom must also evaluate some other alternatives. His client is considering spending $8,000 on home improvements this year, and hence he would have only $2,000 to invest. In this situation, Toms client plans to invest an additional $2,000 at the end of each year for the following 4 years, for a total of 5 payments of $2,000 each. A final possibility is that the client might spend the entire $10,000 on home improvements and then borrow funds for his daughters first year of college.

1. Consider a 5 year, $10,000 CD.

a. What is its value at maturity (future value) if it pays 10.0 percent (annual) interest? b. What would be the future value if the CD pays 5.0 percent? If it pays 15.0 percent? c. The First National Bank of San Francisco offers CDs with a 10.0 percent nominal (stated) interest rate but compounded semiannually. What is the effective annual rate on such a CD? What would its future value be? d. Pacific Trust offers 10.0 percent CDs with daily compounding. What is such a CDs effective annual rate and its value at maturity? e. What nominal rate would the First National Bank have to offer to make its semiannual compounding CD competitive with Pacifics daily-compounding CD?