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Question #1 of 78 Question ID: 1456158 Given the following cash flow stream: End of Year Annual Cash Flow $4,000 $2,000 -0- -$1,000 Using a 10% discount rate, the present value of this cash flow stream is: A) $3,636.00 B) $4,606.00 C) $3,415.00 Explanation PV(1): N = 1; I/Y = 10; FV = -4,000; PMT = 0; CPT → PV = 3,636 PV(2): N = 2; I/Y = 10; FV = -2,000; PMT = 0; CPT → PV = 1,653 PV(3): PV(4): N = 4; I/Y = 10; FV = 1,000; PMT = 0; CPT → PV = -683 Total PV = 3,636 + 1,653 + – 683 = 4,606 (Module 1.2, LOS 1.c) Question #2 of 78 Question ID: 1456215 Peter Wallace wants to deposit $10,000 in a bank certificate of deposit (CD) Wallace is considering the following banks: Bank A offers 5.85% annual interest compounded annually Bank B offers 5.75% annual interest rate compounded monthly Bank C offers 5.70% annual interest compounded daily Which bank offers the highest effective interest rate and how much? A) Bank C, 5.87% B) Bank A, 5.85% C) Bank B, 5.90% Explanation Effective interest rates: Bank A = 5.85 (already annual compounding) Bank B, nominal = 5.75; C/Y = 12; effective = 5.90 Bank C, nominal = 5.70, C/Y = 365; effective = 5.87 Hence Bank B has the highest effective interest rate (Module 1.1, LOS 1.f) Question #3 of 78 Question ID: 1456194 How much should an investor have in a retirement account on his 65th birthday if he wishes to withdraw $40,000 on that birthday and each of the following 14 birthdays, assuming his retirement account is expected to earn 14.5%? A) $272,977 B) $274,422 C) $234,422 Explanation This is an annuity due so set your calculator to the BGN mode N = 15; I/Y = 14.5; PMT = – 40,000; FV = 0; CPT → PV = 274,422.50 Switch back to END mode (Module 1.3, LOS 1.d) Question #4 of 78 Question ID: 1456223 Assuming an annual rate of interest of 11% compounded quarterly, the future value of $8,000 invested for two years is closest to: A) $9,760 B) $9,857 C) $9,939 Explanation The $8,000 investment will compound interest over quarters The rate per quarter is 11% / = 2.75% Therefore, = FV PV(1+r)n = 8,000 × 1.02758 = 9,939 Calculator inputs: I/Y = 2.75; N = 8; PV = 8,000; PMT = 0; CPT FV = –9,939.04 (Module 1.1, LOS 1.e) Question #5 of 78 Question ID: 1456219 A local bank advertises that it will pay interest at the rate of 4.5%, compounded monthly, on regular savings accounts What is the effective rate of interest that the bank is paying on these accounts? A) 4.59% B) 4.50% C) 4.65% Explanation (1 + 0.045 / 12)12 – = 1.0459 – = 0.0459 (Module 1.1, LOS 1.f) Question #6 of 78 Question ID: 1456178 The future value of $10,000 invested for years, if the annual interest rate is 8%, compounded monthly, is closest to: A) $14,000 B) $14,700 C) $14,900 Explanation The investment will compound over × 12 = 60 months The rate per month is 8% / 12 = 0.67% Therefore, FV = $10,000 × (1 + 0.08 / 12)60 = $14,898.46 This is closest to $14,900 Using the calculator: N = 60; PV = -$10,000; I/Y = 0.66667 (8% / 12 months); PMT = 0; CPT → FV = $14,898.46 (Module 1.2, LOS 1.c) Question #7 of 78 Question ID: 1456210 A stated interest rate of 9% compounded quarterly results in an effective annual rate closest to: A) 9.3% B) 9.4% C) 9.2% Explanation Quarterly rate = 0.09 / = 0.0225 Effective annual rate = (1 + 0.0225)4 – = 0.09308, or 9.308% (Module 1.1, LOS 1.f) Question #8 of 78 Question ID: 1456204 It will cost $20,000 a year for four years when an 8-year old child is ready for college How much should be invested today if the child will make the first of four annual withdrawals 10years from today? The expected rate of return is 8% A) $33,138 B) $30,683 C) $66,243 Explanation First, find the present value of the college costs as of the end of year (Remember that the PV of an ordinary annuity is as of time = If the first payment is in year 10, then the present value of the annuity is indexed to the end of year 9) N = 4; I/Y = 8; PMT = 20,000; CPT → PV = $66,242.54 Second, find the present value of this single sum: N = 9; I/Y = 8; FV = 66,242.54; PMT = 0; CPT → PV = 33,137.76 (Module 1.3, LOS 1.d) Question #9 of 78 Question ID: 1456217 What is the effective annual rate if the stated rate is 12% compounded quarterly? A) 12.55% B) 57.35% C) 11.49% Explanation If the stated rate is 12%, then the effective quarterly (period) rate is 12% / = 3% The effective annual rate is, therefore, (1 + period rate)# periods in a year – EAR = [1 + (0.12 / 4)]4 – = 12.55% (Module 1.1, LOS 1.f) Question #10 of 78 Question ID: 1456172 If $2,000 a year is invested at the end of each of the next 45 years in a retirement account yielding 8.5%, the amount the investor will have after 45 years is closest to: A) $900,000 B) $270,000 C) $180,000 Explanation N = 45; PMT = –2,000; PV = 0; I/Y = 8.5%; CPT → FV = $901,060.79 (Module 1.2, LOS 1.c) Question #11 of 78 Question ID: 1456170 Wortel Industries has preferred stock outstanding that paying an annual dividend of $3.75 per share If an investor wants to earn a rate of return of 8.5%, how much should he be willing to pay for a share of Wortel preferred stock? A) $31.88 B) $44.12 C) $42.10 Explanation To calculate the price, we need to discount the future dividend stream at the investor's required return The stream of dividends is a perpetuity (a fixed dividend each year forever) Given the PV of a perpetuity = cash flow / discount rate Then price = $3.75 / 0.085 = $44.12 (Module 1.2, LOS 1.c) Question #12 of 78 Question ID: 1456148 Selmer Jones has just inherited some money and wants to set some of it aside for a vacation in Hawaii one year from today His bank will pay him 5% interest on any funds he deposits In order to determine how much of the money must be set aside and held for the trip, he should use the 5% as a: A) discount rate B) opportunity cost C) required rate of return Explanation He needs to figure out how much the trip will cost in one year, and use the 5% as a discount rate to convert the future cost to a present value Thus, in this context the rate is best viewed as a discount rate (Module 1.1, LOS 1.a) Question #13 of 78 Question ID: 1456163 The future value a 10-year annuity paying an annual sum of $10,000 at the end of each year given a discount rate of 10% would be: A) $100,000 B) $159,374.00 C) $175,312.00 Explanation N = 10; I/Y = 10; PMT = –10,000; PV = 0; CPT → FV = $159,374 (Module 1.2, LOS 1.c) Question #14 of 78 Question ID: 1456184 An investor makes 48 monthly payments of $500 each beginning today into an account that will have a value of $29,000 at the end of four years The stated annual interest rate is closest to: A) 10.00% B) 9.00% C) 9.50% Explanation Because this is an annuity due (payments at the start of each period) the calculator must first be set to BGN mode N = 48; PMT = 500; FV = –29,000; PV = 0; CPT I/Y = 0.7532 This percentage is a monthly rate because the time periods were entered as 48 months It must be converted to a stated annual percentage rate (APR) by multiplying by the number of compounding periods per year: 0.7532 × 12 = 9.04% (Module 1.2, LOS 1.c) Question #15 of 78 Question ID: 1456218 Other things equal, as the number of compounding periods increases, what is the effect on the effective annual rate (EAR)? A) EAR increases B) EAR decreases C) EAR remains the same Explanation The EAR increases with the frequency of compounding (Module 1.1, LOS 1.f) Question #16 of 78 Question ID: 1456175 Given investors require an annual return of 12.5%, a perpetual bond (i.e., a bond with no maturity/due date) that pays $87.50 a year in interest should be valued at: A) $70 B) $1,093 C) $700 Explanation 87.50 ÷ 0.125 = $700 (Module 1.2, LOS 1.c) Question #17 of 78 Question ID: 1462763 Five years ago, an investor borrowed $5,000 from a financial institution that charged a 6% annual interest rate, and he immediately took his family to live in Nepal He made no payments during the time he was away When he returned, he agreed to repay the original loan plus the accrued interest by making five end-of-year payments starting one year after he returned If the interest rate on the loan is held constant at 6% per year, what annual payment must the invstor make in order to retire the loan? A) $1,638.23 B) $1,588.45 C) $1,338.23 Explanation With no interest paid on the original $5,000 loan, at 6% in five years the loan balance will be: New loan balance = $5,000(1.06)5 = $6,691.13 or PV = 5,000; I/Y = 6; N = 5; PMT = 0; CPT → FV = –$6,691.13 $6,691.13 is the loan that has to be retired over the next five years The financial calculator solution is: PV = 6,691.13; I/Y = 6; N = 5; FV = 0; CPT → PMT You obtain PMT = –1,588.45 (Module 1.2, LOS 1.c) Question #18 of 78 Question ID: 1456167 A firm is evaluating an investment that promises to generate the following annual cash flows: End of Year Cash Flows $5,000 $5,000 $5,000 $5,000 $5,000 -0- -0- $2,000 $2,000 Given BBC uses an 8% discount rate, this investment should be valued at: A) $23,529.00 B) $19,963.00 C) $22,043.00 Explanation PV(1 - 5): N = 5; I/Y = 8; PMT = -5,000; FV = 0; CPT → PV = 19,963 PV(6 - 7): PV(8): N = 8; I/Y = 8; FV = -2,000; PMT = 0; CPT → PV = 1,080 PV(9): N = 9; I/Y = 8; FV = -2,000; PMT = 0; CPT → PV = 1,000 Total PV = 19,963 + + 1,080 + 1,000 = 22,043 (Module 1.2, LOS 1.c) Question #19 of 78 Question ID: 1456155 If 10 equal annual deposits of $1,000 are made into an investment account earning 9% starting today, how much will you have in 20 years? A) $39,204 B) $42,165 C) $35,967 Explanation Switch to BGN mode PMT = –1,000; N = 10, I/Y = 9, PV = 0; CPT → FV = 16,560.29 Remember the answer will be one year after the last payment in annuity due FV problems Now PV10 = 16,560.29; N = 10; I/Y = 9; PMT = 0; CPT → FV = 39,204.23 Switch back to END mode (Module 1.2, LOS 1.c) Question #20 of 78 Question ID: 1456156 An annuity will pay eight annual payments of $100, with the first payment to be received three years from now If the interest rate is 12% per year, what is the present value of this annuity? The present value of: A) an ordinary annuity of periods at 12% B) C) a lump sum discounted for years, where the lump sum is the present value of an ordinary annuity of periods at 12% a lump sum discounted for years, where the lump sum is the present value of an ordinary annuity of periods at 12% Explanation ... costs as of the end of year (Remember that the PV of an ordinary annuity is as of time = If the first payment is in year 10 , then the present value of the annuity is indexed to the end of year... paying on these accounts? A) 4.59% B) 4.50% C) 4.65% Explanation (1 + 0.045 / 12 )12 – = 1. 0459 – = 0.0459 (Module 1. 1, LOS 1. f) Question #6 of 78 Question ID: 14 5 617 8 The future value of $10 ,000... Question ID: 14 5 616 3 The future value a 10 -year annuity paying an annual sum of $10 ,000 at the end of each year given a discount rate of 10 % would be: A) $10 0,000 B) $15 9,374.00 C) $17 5, 312 .00 Explanation