数量方法：基本概念(三)及答案解析.doc

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1、数量方法：基本概念(三)及答案解析(总分：25.00，做题时间：90 分钟)一、B单项选择题/B(总题数：1，分数：25.00)Use a stated rate of 9 percent compounded periodically to answer the following three questions. Select the choice that is the closest to the correct answer.（分数：25.00）(1).The semi - annual effective rate is : A.9.20%. B.9.00%. C. 10.25%.

2、（分数：1.00）A.B.C.D.(2).An investment offers $100 per year forever. If Peter Wallaces required rate of return on this investment is 10 percent, how much is this investment worth to him? A. $500. B. $100 million. C. $1000.（分数：1.00）A.B.C.D.(3).The quarterly effective rate is: A.9.31%. B.9.00%. C.9.20%.（分

3、数：1.00）A.B.C.D.(4).One year ago, an investor made five separate investments with the invested amounts and returns shown below. What is the arithmetic and geometric mean return on all of the investors investments ? Investment Invested Amount Return(%)A 10000 12B 10000 14C 10000 9D 20000 13E 20000 7 A

4、. 11.64 10.78 B. 1.64 10.97 C. 11.00 10.97（分数：1.00）A.B.C.D.(5).How much should an investor have in a retirement account on his 65th birthday if he wishes to withdraw $ 40000 on that birthday and each of the following 14 birthdays, assuming his retirement account is expected to earn 14.5 percent? A.

5、$ 234422. B. $ 274422. C. $ 272977.（分数：1.00）A.B.C.D.(6).What is the main difference between descriptive statistics and inferential statistics? A. Descriptive statistics are used to make forecasts about the likelihood of upcoming events while inferential statistics are used to summarize any data set.

6、 B. Descriptive statistics are calculations based on small samples while inferential statistics are calculations based on large samples. C. Descriptive statistics are used to summarize a large data set while inferential statistics involves procedures used to make forecasts or judgments about a large

7、 data set by examining a smaller sample.（分数：1.00）A.B.C.D.(7).Concerning an ordinary annuity and an annuity due with the same payments and positive interest rate, which of the following statements is TRUE? A. There is no relationship. B. The present value of the ordinary annuity is equal to annuity d

8、ue. C. The present value of the ordinary annuity is less than an annuity due.（分数：1.00）A.B.C.D.(8).Which of the following best describes a frequency distribution? A frequency distribution is a grouping of: A. data into intervals (classes) so that the number of observations in each of the non - overla

9、pping intervals (classes) can be seen and tallied. B. selected data into intervals (classes) so that the number of observations in each of the non - overlapping intervals (classes) can be seen and tallied. C. dependent intervals (classes) so that they can be seen and tallied.（分数：1.00）A.B.C.D.(9).The

10、re is a 40% chance that the economy will be good next year and a 60% chance that it will be bad. If the economy is good, there is a 50% chance of a bull market, a 30% chance of a normal market, and a 20% chance of a bear market. If the economy is bad, there is a 20% chance of a bull market, a 30% ch

11、ance of a normal market, and a 50% chance of a bear market. What is the joint probability of a good economy and a bull market? A. 12%. B.20%. C.32%.（分数：1.00）A.B.C.D.(10).An investment with a cost of $ 5000 is expected to have cash inflows of $ 3000 in year 1, and $4000 in year 2. The internal rate o

12、f return (IRR) for this investment is closest to. A. 15%. B. 30%. C. 25%.（分数：1.00）A.B.C.D.(11).A local bank offers an account that pays 8 percent, compounded quarterly, for any deposits of $10000 or more that are left in the account for a period of 5 years. The effective annual rate of interest on t

13、his account is. A. 9.01%. B.4.65%. C. 8.24%.（分数：1.00）A.B.C.D.(12).The financial manager at Kyser Jones is considering two mutually exclusive projects with the following projected cash flows: Projected Cash FlowsYear Project M Project Z0 -$60000 -$600001 22500 02 22500 03 22500 04 22500 111000If Kyse

14、r Jones required rate of return is 11 percent, which project would be chosen and why? A. Project M, because it has the higher internal rate of return. B. Project Z, because it has the higher net present value. C. Both projects, because their net present values are positive.（分数：1.00）A.B.C.D.(13).A di

15、stribution that is more peaked than normal is: A. skewed. B. platykurtic. C. leptokurtic.（分数：1.00）A.B.C.D.(14).Given P(X =2, Y= 10) =0.3, P(X=6, Y=2.5) =0.4, and P(X =10,Y=0)=0.3, then Cov(XY) is: A. -12.0. B. 24.0. C. 6.0.（分数：1.00）A.B.C.D.(15).For a stock, which of the following is NOT a random var

16、iable? A. Its most recent closing price. B. Its P/E ratio. C. Its stock symbol.（分数：1.00）A.B.C.D.(16).An investor sold a 30 - year bond at a price of $ 850 after he purchased it at $ 800 a year ago. He received $ 50 of interest at the time of the sale. The annualized holding period return is: A. 15.0

17、%. B. 10.0%. C. 12.5%.（分数：1.00）A.B.C.D.(17).Use the results from the following survey of 500 firms to answer the question. Number of Employees Frequency300 up to 400 40400 up to 500 62500 up to 600 78600 up to 700 101700 up to 800 131800 up to 900 88The cumulative relative frequency of the second in

18、terval (400 to 500) is: A. 20.4%. B. 10.2%. C. 36.0%.（分数：1.00）A.B.C.D.(18).Given Cov (X,Y) = 1000000. What does this indicate about the relationship between X and Y? A. It is strong and positive. B. It is weak and positive. C. Only that it is positive.（分数：1.00）A.B.C.D.(19).If the outcome of event A

19、is not affected by event B, then events A and B are said to be: A. mutually exclusive. B. statistically independent. C. collectively exhaustive.（分数：1.00）A.B.C.D.(20).Steve Hall wants to give his son a new car for his graduation. If the cost of the car is $15000 and Hall finances 80 percent of the va

20、lue of the car for 36 months at 8 percent annual interest, his monthly payments will be: A. $289. B.$413. C. $376.（分数：1.00）A.B.C.D.(21).It will cost $ 20000 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 fo

21、ur annual withdrawals 10 - years from today? The expected rate of return is 8 percent. A. $ 30683. B. $ 66243. C. $ 33138.（分数：1.00）A.B.C.D.(22).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 % interes

22、t 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(n). A. opportunity cost. B. discount rate. C. required rate of return.（分数：1.00）A.B.C.D.(23).Consider a 10 - year annuity that promises to pay out $10000 per year

23、; given this is an ordinary annuity and that an investor can earn 10 percent on her money, the future value of this annuity, at the end of 10 years, would be: A. $159374. B. $175312. C. $152500.（分数：1.00）A.B.C.D.(24).A joint probability of A and B must always be: A. less than or equal to the conditio

24、nal probability of A given B. B. greater than or equal to the conditional probability of A given B. C. greater than or equal to than the probability of A or B.（分数：1.00）A.B.C.D.(25).If the odds against an event occurring are twelve to one, what is the probability that it will occur? A. 0.0769. B. 0.0

25、833. C. 0.9167.（分数：1.00）A.B.C.D.数量方法：基本概念(三)答案解析(总分：25.00，做题时间：90 分钟)一、B单项选择题/B(总题数：1，分数：25.00)Use a stated rate of 9 percent compounded periodically to answer the following three questions. Select the choice that is the closest to the correct answer.（分数：25.00）(1).The semi - annual effective rate is

26、 : A.9.20%. B.9.00%. C. 10.25%.（分数：1.00）A. B.C.D.解析：First, we need to calculate the periodic rate, or 0.09/2=0.045.Then, the effective semi - annual rate=(1+0.045)2-1=0.09203, or 9.20%.(2).An investment offers $100 per year forever. If Peter Wallaces required rate of return on this investment is 10

27、percent, how much is this investment worth to him? A. $500. B. $100 million. C. $1000.（分数：1.00）A.B.C. D.解析：For a perpetuity, PV=PMT/I=100/0.10=1000.(3).The quarterly effective rate is: A.9.31%. B.9.00%. C.9.20%.（分数：1.00）A. B.C.D.解析：First, we need to calculate the periodic rate, or 0.09/4=0.0225.Then

28、, the effective annual rate = (1+0.0225)4-1=0.09308, or 9.31%.(4).One year ago, an investor made five separate investments with the invested amounts and returns shown below. What is the arithmetic and geometric mean return on all of the investors investments ? Investment Invested Amount Return(%)A 1

29、0000 12B 10000 14C 10000 9D 20000 13E 20000 7 A. 11.64 10.78 B. 1.64 10.97 C. 11.00 10.97（分数：1.00）A.B.C. D.解析：Arithmetic Mean: 12 + 14 +9 + 13 +7 =55; 55/5 = 11 ; Geometric Mean: *(5).How much should an investor have in a retirement account on his 65th birthday if he wishes to withdraw $ 40000 on th

30、at birthday and each of the following 14 birthdays, assuming his retirement account is expected to earn 14.5 percent? A. $ 234422. B. $ 274422. C. $ 272977.（分数：1.00）A.B. C.D.解析：This is an annuity due so set your calculator to the BGN mode. N=15; I/Y=14.5; PMT=-40000; FV=0; CPTPV=274422.50. Switch ba

31、ck to END mode.(6).What is the main difference between descriptive statistics and inferential statistics? A. Descriptive statistics are used to make forecasts about the likelihood of upcoming events while inferential statistics are used to summarize any data set. B. Descriptive statistics are calcul

32、ations based on small samples while inferential statistics are calculations based on large samples. C. Descriptive statistics are used to summarize a large data set while inferential statistics involves procedures used to make forecasts or judgments about a large data set by examining a smaller samp

33、le.（分数：1.00）A.B.C. D.解析：Descriptive statistics are used to summarize a large data set while inferential statistics are based on procedures used to make forecasts or judgments about a large data set by examining a smaller set of data.(7).Concerning an ordinary annuity and an annuity due with the same

34、 payments and positive interest rate, which of the following statements is TRUE? A. There is no relationship. B. The present value of the ordinary annuity is equal to annuity due. C. The present value of the ordinary annuity is less than an annuity due.（分数：1.00）A.B.C. D.解析：With a positive interest r

35、ate, the present value of an ordinary annuity is less than the present value of an annuity due. The first cash flow in an annuity due is at the beginning of the period, while in an ordinary annuity, the first cash flow occurs at the end of the period. Therefore, each cash flow of the ordinary annuit

36、y is discounted one period more.(8).Which of the following best describes a frequency distribution? A frequency distribution is a grouping of: A. data into intervals (classes) so that the number of observations in each of the non - overlapping intervals (classes) can be seen and tallied. B. selected

37、 data into intervals (classes) so that the number of observations in each of the non - overlapping intervals (classes) can be seen and tallied. C. dependent intervals (classes) so that they can be seen and tallied.（分数：1.00）A. B.C.D.解析：A frequency distribution is a tabular presentation of statistical

38、 data that aids the analysis of large data sets.(9).There is a 40% chance that the economy will be good next year and a 60% chance that it will be bad. If the economy is good, there is a 50% chance of a bull market, a 30% chance of a normal market, and a 20% chance of a bear market. If the economy i

39、s bad, there is a 20% chance of a bull market, a 30% chance of a normal market, and a 50% chance of a bear market. What is the joint probability of a good economy and a bull market? A. 12%. B.20%. C.32%.（分数：1.00）A.B. C.D.解析：Joint probability is the probability that both events, in this case the econ

40、omy being good and the occurrence of a bull market, happen at the same time. Joint probability is computed by multiplying the individual event probabilities together : (0.40)(0.50)=0.20 or 20 percent.(10).An investment with a cost of $ 5000 is expected to have cash inflows of $ 3000 in year 1, and $

41、4000 in year 2. The internal rate of return (IRR) for this investment is closest to. A. 15%. B. 30%. C. 25%.（分数：1.00）A.B.C. D.解析：The IRR is the discount rate that makes the net present value of the investment equal to 0.This means - $ 5000 + $ 3000/( 1 + IRR) + $ 4000/( 1 + IRR)2 = 0One way to compu

42、te this problem is to use trial and error with the existing answer choices and choose the discount rate that makes the PV of the cash flows closest to 5000.$ 3000/1.25 + $ 4000/1.252 = 4960.Alternatively: CF0 = -5000, CF1 =3000, CF2 =4000, CPT IRR =24.3%.(11).A local bank offers an account that pays

43、 8 percent, compounded quarterly, for any deposits of $10000 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. 9.01%. B.4.65%. C. 8.24%.（分数：1.00）A.B.C. D.解析：(1+periodic rate) m-1=(1.02)4-1=8.24%.(12).The financial manager at Ky

44、ser Jones is considering two mutually exclusive projects with the following projected cash flows: Projected Cash FlowsYear Project M Project Z0 -$60000 -$600001 22500 02 22500 03 22500 04 22500 111000If Kyser Jones required rate of return is 11 percent, which project would be chosen and why? A. Proj

45、ect M, because it has the higher internal rate of return. B. Project Z, because it has the higher net present value. C. Both projects, because their net present values are positive.（分数：1.00）A.B. C.D.解析：Since the projects are mutually exclusive, only one of the projects may be choosen. Project Z has

46、the higher NPV. On the exam, always use NPV for choosing between nutually exclusive projects. Cash Flow Input ValuesProject M Project ZCF0 -60000 -60000CF1 22500 0F1 4 3CF2 111000F2 1Output ValuesProject M Project ZNPV $9805 $13119IRR 18.45% 16.62%(13).A distribution that is more peaked than normal

47、is: A. skewed. B. platykurtic. C. leptokurtic.（分数：1.00）A.B.C. D.解析：A distribution that is more peaked than normal is leptokurtic. A distribution that is flatter than normal is platykurtic.(14).Given P(X =2, Y= 10) =0.3, P(X=6, Y=2.5) =0.4, and P(X =10,Y=0)=0.3, then Cov(XY) is: A. -12.0. B. 24.0. C.

48、 6.0.（分数：1.00）A. B.C.D.解析：The expected values are: E(X) =(0.32)+(0.46)+(0.310)=6 and E(Y) =(0.310.0)+(0.42.5)+(0.30.0)=4. The covariance is Cov (XY) =0.3(2-6)(10-4)+0.4(6-6)(2.5-4)+0.3(10-6)(0-4)= -12.(15).For a stock, which of the following is NOT a random variable? A. Its most recent closing price

49、. B. Its P/E ratio. C. Its stock symbol.（分数：1.00）A.B.C. D.解析：A random variable must be a number. Sometimes there is an obvious method for assigning a number, such as when the random variable is a number itself, like a P/E ratio. A stock symbol of a randomly selected stock could have a number assigned to it l