# Finance Exam #2

 ________ is the amount earned on a deposit that has become the part of the principal at the end of a specified time period. Compound Interest The future value of \$100 received today and deposited at 6 percent for four years is ________. \$126 The future value of \$200 received today and deposited at 8 percent for three years is ________. \$252 The present value of \$100 to be received 10 years from today, assuming an opportunity cost of 9 percent, is ________. \$42 The amount of money that would have to be invested today at a given interest rate over a specified period in order to equal a future amount is called ________. Present Value The present value of \$200 to be received 10 years from today, assuming an opportunity cost of 10 percent, is ________. \$77 The future value of a dollar ________ as the interest rate increases and ________ the further in the future an initial deposit is to be received Increases; Increases The annual rate of return is referred to as the ________. discount rate If you expect to retire in 30 years, live on \$50,000 per year and expect the inflation to average 3% over the next 30 years, what amount of annual income will you need to live at the same comfort level in 30 years? \$121,363 Calculate the future value of \$4,600 received today if it is deposited at 9 percent for three years. FV=PV(1+r)^n=\$4,600(1.09)^3=\$5,957 Calculate the present value of \$89,000 to be received in 15 years, assuming an opportunity cost of 14 percent. PV=89,000(1.14)^-15=\$12,469 Aunt Tillie has deposited \$33,000 today in an account which will earn 10 percent annually. She plans to leave the funds in this account for seven years earning interest. If the goal of this deposit is to cover a future obligation of \$65,000, what recommendation would you make to Aunt Tillie? FV = 33,000(1.1)^7 = \$64,308Aunt Tillie will only have \$64,308 at the end of seven years under the stated arrangement. She must find an account with a higher interest rate or deposit a larger sum today.The amount Aunt Tillie should invest today to receive \$65,000 after 7 years, PV = 65,000 / (1.1)^7 = \$33,355.28 China Manufacturing Agents, Inc. is preparing a five-year plan. Today, sales are \$1,000,000. If the growth rate in sales is projected to be 10 percent over the next five years, what will the dollar amount of sales be in year five? FV = 1,000,000(1.1)^5 = \$1,610,510 Colin has inherited \$6,000 from the death of Grandma Anna. He would like to use this money to buy his mom Hayley a new scooter costing \$7,000, two years from now. Will Colin have enough money to buy the gift if he deposits his money in an account paying 8 percent compounded semiannually? n = 2, m = 2, r = 8%FV = 6,000(1+.08/2)^2 × 2 = 6000(1.04)^4 = \$7,019Yes, Colin will have enough money to buy the scooter Dan and Jia are newlyweds and have just purchased a condominium for \$70,000. Since the condo is very small, they hope to move into a single-family house in 5 years. How much will their condo worth in 5 years if inflation is expected to be 8 percent? PV = \$70,000, r = 8%, n = 5FV = 70,000(1.08)^5 = \$102,853 Congratulations! You have just won the lottery! However, the lottery bureau has just informed you that you can take your winnings in one of two ways. Choice X pays \$1,000,000. Choice Y pays \$1,750,000 at the end of five years from now. Using a discount rate of 5 percent, based on present values, which would you choose? Using the same discount rate of 5 percent, based on future values, which would you choose? What do your results suggest as a general rule for approaching such problems? (Make your choices based purely on the time value of money.) The PV of X = \$1,000,000; The PV of Y = \$1,371,000; The FV of X = \$1,276,000; The FV of Y = \$1,500,000. Based on both present values and future values, B is the better choice. Finding present values and future values are simply reverse processes of one another, and that choosing between two lump sums based on PV will always give the same result as choosing between the same two lump sums based on FV. Which of the following is true of annuities? An annuity due is an equal stream of cash flows is paid or received at the beginning of each period. The present value of a \$25,000 perpetuity at a 14 percent discount rate is ________. \$178,571 An annuity with an infinite life is called a(n) ________. perpetuity The present value of a \$20,000 perpetuity at a 7 percent discount rate is ________. \$285,714 A(n) ________ is an annuity with an infinite life making continual annual payments. perpetuity Bill plans to fund his individual retirement account (IRA) with the maximum contribution of \$2,000 at the end of each year for the next 20 years. If Bill can earn 12 percent on his contributions, how much will he have at the end of the twentieth year? \$144,104 Dan plans to fund his individual retirement account (IRA) with the maximum contribution of \$2,000 at the end of each year for the next 10 years. If Dan can earn 10 percent on his contributions, how much will he have at the end of the tenth year? \$31,874 In comparing an ordinary annuity and an annuity due, which of the following is true? The future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity. The future value of a \$2,000 annuity due deposited at 8 percent compounded annually for each of the next 10 years is ________. \$31,291 The future value of a \$10,000 annuity due deposited at 12 percent compounded annually for each of the next 5 years is ________. \$71,152 The future value of an ordinary annuity of \$1,000 each year for 10 years, deposited at 3 percent, is ________. \$11,464. The future value of an ordinary annuity of \$2,000 each year for 10 years, deposited at 12 percent, is ________. \$35,098 A college received a contribution to its endowment fund of \$2 million. It can never touch the principal, but can use the earnings. At an assumed interest rate of 9.5 percent, how much can the college earn to help its operations each year? \$190,000 If the present value of a perpetual income stream is increasing, the discount rate must be ________. decreasing The present value of an ordinary annuity of \$350 each year for five years, assuming an opportunity cost of 4 percent, is ________. \$1,558 The present value of an ordinary annuity of \$2,350 each year for eight years, assuming an opportunity cost of 11 percent, is ________. \$12,093 A generous benefactor to a local ballet plans to make a one-time endowment that would provide the ballet with \$150,000 per year into perpetuity. The rate of interest is expected to be 5 percent for all future time periods. How large must the endowment be? \$3,000,000 A generous philanthropist plans to make a one-time endowment to a renowned heart research center which would provide the facility with \$250,000 per year into perpetuity. The rate of interest is expected to be 8 percent for all future time periods. How large must the endowment be? \$3,125,000 Mary will receive \$12,000 per year for the next 10 years as royalty for her work on a finance book. What is the present value of her royalty income if the opportunity cost is 12 percent? \$ 67,800 To pay for her college education, Gina is saving \$2,000 at the beginning of each year for the next eight years in a bank account paying 12 percent interest. How much will Gina have in that account at the end of 8th year? \$27,552 James plans to fund his individual retirement account, beginning today, with 20 annual deposits of \$2,000, which he will continue for the next 20 years. If he can earn an annual compound rate of 8 percent on his deposits, the amount in the account upon retirement will be \$98,846
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