1. The Time Value of Money

30 months ago, Desmond placed $1000 into an account which practises continuous compounding at a guaranteed rate of 8% per year. If he withdraws the full amount today, how much can he withdraw? (Round off to the nearest dollar)

1221 (30 mths = 2.5 years FV = 1000 x e^(0.08×2.5) = 1221)

2. An interest rate from which the inflation premium has been subtracted is known as: A. a real interest rate. B. a risk-free interest rate. C. a real risk-free interest rate

A

Question #19 of 81 Vega research has been conducting investor polls for Third State Bank. They have found the most investors are not willing to tie up their money in a 1-year (2-year) CD unless they receive at least 1.0% (1.5%) more than they would on an ordinary savings account. If the savings account rate is 3%, and the bank wants to raise funds with 2-year CDs, the yield must be at least: A) 4.5%, and this represents a required rate of return. B) 4.5%, and this represents a discount rate. C) 4.0%, and this represents a required rate of return.

A

Question #29 of 81 How much would the following income stream be worth assuming a 12% discount rate? $100 received today. $200 received 1 year from today. $400 received 2 years from today. $300 received 3 years from today. A) $810.98. B) $721.32. C) $1,112.44.

A

Question #30 of 81 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

A

Question #31 of 81 Elise Corrs, hedge fund manager and avid downhill skier, was recently granted permission to take a 4 month sabbatical. During the sabbatical, (scheduled to start in 11 months), Corrs will ski at approximately 12 resorts located in the Austrian, Italian, and Swiss Alps. Corrs estimates that she will need $6,000 at the beginning of each month for expenses that month. (She has already financed her initial travel and equipment costs.) Her financial planner estimates that she will earn an annual rate of 8.5% during her savings period and an annual rate of return during her sabbatical of 9.5%. How much does she need to put in her savings account at the end of each month for the next 11 months to ensure the cash flow she needs over her sabbatical? Each month, Corrs should save approximately: A) $2,080. B) $2,065. C) $2,070

A

Question #39 of 81 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

A

Question #12 of 81 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) $234,422. B) $274,422. C) $272,977.

B

Question #15 of 81 A firm is evaluating an investment that promises to generate the following annual cash flows: End of Year Cash Flows 1 $5,000 2 $5,000 3 $5,000 4 $5,000 5 $5,000 6 -0- 7 -0- 8 $2,000 9 $2,000 Given BBC uses an 8% discount rate, this investment should be valued at: A) $19,963.00 B) $22,043.00 C) $23,529.00

B

Question #16 of 81 Given a 5% discount rate, the present value of $500 to be received three years from today is: A) $400. B) $432. C) $578.

B

Question #20 of 81 Three years from now, an investor will deposit the first of eight $1,000 payments into a special fund. The fund will earn interest at the rate of 5% per year until the third deposit is made. Thereafter, the fund will return a reduced interest rate of 4% compounded annually until the final deposit is made. How much money will the investor have in the fund at the end of ten years assuming no withdrawals are made? A) $8,872.93. B) $9,251.82. C) $9,549.11

B

Question #25 of 81 A local bank offers an account that pays 8%, compounded quarterly, for any deposits of $10,000 or more that are left in the account for a period of 5 years. The effective annual rate of interest on this account is: A) 4.65%. B) 8.24%. C) 9.01%.

B

Question #28 of 81 The real risk-free rate can be thought of as: A) approximately the nominal risk-free rate plus the expected inÖation rate. B) approximately the nominal risk-free rate reduced by the expected inÖation rate. C) exactly the nominal risk-free rate reduced by the expected inÖation rate.

B

Question #40 of 81 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%

B

6. An investor will receive an annuity of $4,000 a year for 10 years. The first payment is to be received five years from today. At a 9% discount rate, this annuity's worth today is closest to: A. $16,684. B. $18,186. C. $25,671.

B (Two steps: (1) Find the PV of the 10-year annuity: N = 10; I/Y = 9; PMT = -4,000; FV = 0; CPT → PV = 25,670.63. This is the present value as of the end of Year 4; (2) Discount PV of the annuity back four years: N =4; PMT = 0; FV = -25,670.63; I/Y = 9; CPT → PV = 18,185.72.)

6 months from now, Ravi would like to place $3000 into a fixed rate savings account which gives a quoted interest of 6% per year. The interest is paid out quarterly. Assuming there are no other cashflows, how much will be in the account 2 years from today? $3274 $3280 $3379

B (Compounding frequency is quarterly.N = 1.5 x 4 = 6r = 6 / 4 = 1.5%FV = 3000 x (1 + 0.015)^6 = $3280)

Lena decided to forego a lump sum savings plan where she puts in $50,000 today and gets back $70,000 in 5 year's time. What is the opportunity cost (in % terms) of the $50,000 to Lena? A. 8% B. 40% C. 28.6%

B (Opportunity cost = Interest foregone / Principle = 20000/50000 = 40%)

1. An analyst estimates that XYZ's earnings will grow from $3.00 a share to $4.50 per share over the next eight years. The rate of growth in XYZ's earnings is closest to: A. 4.9%. B. 5.2%. C. 6.7%

B (N = 8; PV = -3; FV = 4.50; PMT = 0; CPT → I/Y = 5.1989)

4. If $10,000 is invested today in an account that earns interest at a rate of 9.5%, what is the value of the equal withdrawals that can be taken out of the account at the end of each of the next five years if the investor plans to deplete the account at the end of the time period? A. $2,453. B. $2,604. C. $2,750.

B (PV = -10,000; I/Y = 9.5; N = 5; FV = 0; CPT → PMT = $2,604.36)

1. An interest rate is best interpreted as: A. a discount rate or a measure of risk. B. a measure of risk or a required rate of return. C. a required rate of return or the opportunity cost of consumption.

C

Question #13 of 81 The First State Bank is willing to lend $100,000 for 4 years at 12%. Assuming the loan is fully amortizing repayable in six monthly installments, the first payment is closest to:A) $6,000. B) $32,900. C) $16,100

C

Question #22 of 81 Which one of the following statements best describes the components of the required interest rate on a security? A) The real risk-free rate, the default risk premium, a liquidity premium and a premium to reÖect the risk associated with the maturity of the security. B) The nominal risk-free rate, the expected inÖation rate, the default risk premium, a liquidity premium and a premium to reÖect the risk associated with the maturity of the security. C) The real risk-free rate, the expected inÖation rate, the default risk premium, a liquidity premium and a premium to reÖect the risk associated with the maturity of the security.

C

Question #24 of 81 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) $1,338.23. C) $1,588.45.

C

Question #26 of 81 Jim Franklin recently purchased a home for $300,000 on which he made a down payment of $100,000. He obtained a 30-year mortgage to finance the balance on which he pays a fixed annual rate of 6%. If he makes regular, fixed monthly payments, what loan balance will remain just after the 48th payment? A) $186,109. B) $192,444. C) $189,229.

C

Question #4 of 81 Nikki Ali and Donald Ankard borrowed $15,000 to help finance their wedding and reception. The annual payment loan carries a term of seven years and an 11% interest rate. Respectively, the amount of the first payment that is interest and the amount of the second payment that is principal are approximately: A) $1,468; $1,702. B) $1,650; $1,468. C) $1,650; $1,702.

C

Question #7 of 81 Justin Banks just won the lottery and is trying to decide between the annual cash flow payment option or the lump sum option. He can earn 8% at the bank and the annual cash flow option is $100,000/year, beginning today for 15 years. What is the annual cash flow option worth to Banks today? A) $1,080,000.00. B) $855,947.87. C) $924,423.70.

C

Question #9 of 81 An investor has the choice of two investments. Investment A offers interest at 7.25% compounded quarterly. Investment B offers interest at the annual rate of 7.40%. Which investment offers the higher dollar return on an investment of $50,000 for two years, and by how much? A) Investment A oáers a $122.18 greater return. B) Investment B oáers a $36.92 greater return. C) Investment A oáers a $53.18 greater return.

C

Lilian opened a savings account 3 years ago, where she placed an initial deposit of $2000. She placed another $1000 the following year. The account credits daily interest at a quoted interest rate of 3.65% per year. How much is in her account today? $3292 $3301 $3307

C (Daily interest = 3.65 / 365 = 0.01% $2000 is compounded daily for 3 yearsFV1 = 2000 x 1.0001^(365×3) = $2231 $1000 is compounded daily for 2 yearsFV2 = 1000 x 1.0001^(365×2) = $1076 Total in account = $2231 + $1076 = $3307)

3. An investor is looking at a $150,000 home. If 20% must be put down and the balance is financed at a stated annual rate of 9% over the next 30 years, what is the monthly mortgage payment? A. $799.33. B. $895.21. C. $965.55.

C (N = 30 × 12 = 360; I/Y = 9/12 = 0.75; PV = -150,000(1 - 0.2) = -120,000; FV = 0; CPT → PMT = $965.55 (LOS1.e))

2. If $5,000 is invested in a fund offering a rate of return of 12% per year, approximately how many years will it take for the investment to reach $10,000? A. 4 years. B. 5 years. C. 6 years.

C (PV = -5,000; I/Y = 12; FV = 10,000; PMT = 0; CPT → N = 6.12)

effective annual rate (EAR) or effective annual yield (EAY)

The rate of interest that investors actually realize as a result of compounding EAR represents the annual rate of return actually being earned after adjustments have been made for different compounding periods the greater the compounding frequency, the greater the EAR will be in comparison to the stated rate

Cash Flow Additivity Principle

refers to the fact that present value of any stream of cash flows equals the sum of the present values of the cash flows.