Question: 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 daughter's 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 daughter's 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 ways-the 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, Tom's 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 daughter's first year of college.

Now consider the second alternative-5 annual payments of $2,000 each. Assume that the payments are made at the end of each year.

a. What type of annuity is this?

b. What is the future value of this annuity if the payments are invested in an account paying 10.0 percent interest annually?

c. What is the future value if the payments are invested with the First National Bank which offers semiannual compounding?

d. What size payment would be needed to accumulate $20,000 under annual compounding at a 10.0 percent interest rate?

e. What lump sum, if deposited today, would produce the same ending value as in Part b?

f. Suppose the payments are only $1,000 each, but are made every 6 months, starting 6 months from now. What would be the future value if the 10 payments were invested at 10.0 percent annual interest? If they were invested at the First National Bank which offers semiannual compounding?

5. Assume now that the payments are made at the beginning of each period. Repeat the analysis in Question 4.