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Cash flow investment decision Tom Alexander has an opportunity to purchase any of the investments shown in the following table. The purchase price, the amount of the single cash inflow, and its year of receipt are given for each investment. Which purchase recommendations would you make, assuming that Tom can earn 10% on his investments? P518 Calculating deposit needed You put $10,000 in an account earning 5%. After 3 years, you make another deposit into the same account. Four years later (that is, 7 years after your original $10,000 deposit), the account balance is $20,000. What was the amount of the deposit at the end of year 3? LG 2 LG 2 LG 2 202 PART 2 Financial Tools Case Amount of annuity Interest rate Deposit period (years) A $ 2,500 8% 10 B 500 12 6 C 30,000 20 5 D 11,500 9 8 E 6,000 14 30 a. Calculate the future value of the annuity assuming that it is (1) An ordinary annuity. (2) An annuity due. b. Compare your findings in parts a(1) and a(2). All else being identical, which type of annuityordinary or annuity dueis preferable? Explain why. P5-20 Present value of an annuity Consider the following cases. Case Amount of annuity Interest rate Period (years) A $ 12,000 7% 3 B 55,000 12 15 C 700 20 9 D 140,000 5 7 E 22,500 10 5 a. Calculate the present value of the annuity assuming that it is (1) An ordinary annuity. (2) An annuity due. b. Compare your findings in parts a(1) and a(2). All else being identical, which type of annuityordinary or annuity dueis preferable? Explain why. Personal Finance Problem P521 Time valueAnnuities Marian Kirk wishes to select the better of two 10-year annuities, C and D. Annuity C is an ordinary annuity of $2,500 per year for 10 years. Annuity D is an annuity due of $2,200 per year for 10 years. a. Find the future value of both annuities at the end of year 10, assuming that Marian can earn (1) 10% annual interest and (2) 20% annual interest. b. Use your findings in part a to indicate which annuity has the greater future value at the end of year 10 for both the (1) 10% and (2) 20% interest rates. c. Find the present value of both annuities, assuming that Marian can earn (1) 10% annual interest and (2) 20% annual interest. d. Use your findings in part c to indicate which annuity has the greater present value for both (1) 10% and (2) 20% interest rates. e. Briefly compare, contrast, and explain any differences between your findings using the 10% and 20% interest rates in parts b and d. LG 3 LG 3 LG 3 P519 Future value of an annuity For each case in the accompanying table, answer the questions that follow. CHAPTER 5 Time Value of Money 203 Personal Finance Problem P522 Retirement planning Hal Thomas, a 25-year-old college graduate, wishes to retire at age 65. To supplement other sources of retirement income, he can deposit $2,000 each year into a tax-deferred individual retirement arrangement (IRA). The IRA will earn a 10% return over the next 40 years. a. If Hal makes annual end-of-year $2,000 deposits into the IRA, how much will he have accumulated by the end of his sixty-fifth year? b. If Hal decides to wait until age 35 to begin making annual end-of-year $2,000 deposits into the IRA, how much will he have accumulated by the end of his sixty-fifth year? c. Using your findings in parts a and b, discuss the impact of delaying making deposits into the IRA for 10 years (age 25 to age 35) on the amount accumulated by the end of Hals sixty-fifth year. d. Rework parts a, b, and c, assuming that Hal makes all deposits at the beginning, rather than the end, of each year. Discuss the effect of beginning-of-year deposits on the future value accumulated by the end of Hals sixty-fifth year.

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