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1、二、Investment Tools: Quantitative Methods1.A.: Time Value of MoneyQuestion ID: 20976A certain investment product promises to pay $25,458 at the end of 9 years. If an investor feels this investment should produce a rate of return of 14 percent, compounded annually, whats the most he should be willing
2、to pay for it?A.$7,618.B.$8,342.C.$9,426.D.$7,828.D=9; I/Y=14; FV=-25,458; PMT=0; CPT PV=$7,828.Question ID: 20973An investor deposits $4,000 in an account that pays 7.5 percent, compounded annually. How much will this investment be worth after 12 years?A.$9,527.B.$7,600.C.$9,358.D.$5,850.AN=12; I/Y
3、=7.5; PV=-4,000; PMT=0; CPT FV=$9,527.Question ID: 18489If a person needs $20,000 in 5 years from now and interest rates are currently 6% how much do they need to invest today? A.$15,301B.$14,683C.$14,945D.$14,284 CPV=FV/(1+r)n =20000/(1.06)5 = 20000/1.33823 = 14,945 n = 5, i/yr = 6%, PMT = 0, FV =
4、$20,000, Compute PV = -$14,945.16 Question ID: 20978How long will it take $20,000 to grow to $50,000, given an investor can earn 12 percent (compounded annually) on his money?A.5.8 years.B.8.1 years.C.7.5 years.D.6.0 years.BI/Y=12; PV=-20,000; FV=50,000; PMT=0; CPT N=8.08Question ID: 19376A leading
5、brokerage firm has advertised money multiplier certificates that will triple your money in 9 years (i.e., invest $10,000 today, and itll be worth $30,000 in 9 years). Approximately what rate of return will investors be earning on these certificates?A.16.0%.B.8.8%.C.13.0%.D.12.5%.CUsing your calculat
6、or: N=9; PV=-10,000; FV=30,000; PMT=0; CPT I/Y=12.98.Question ID: 19378What is the present value of a 12-year annuity due that pays $5,000 per year, given a discount rate of 7.5 percent?A.$36,577.B.$41,577.C.$38,676.D.$23,857.BUsing your calculator: N=11; I/Y=7.5; PMT=-5,000; FV=0; CPT PV=36,577+5,0
7、00=$41,577. Or set your calculator to BGN mode and N=12; I/Y=7.5; PMT=-5,000; FV=0; CPT PV=$41,577. Question ID: 18492An annuity will pay eight annual payments of $100, with the first payment to be received one year from now. If the interest rate is 12% per year, what is the present value of this an
8、nuity? A.$556.38B.$1,377.57C.$496.76D.$1,229.97 Cn = 8, i/yr = 12%, PMT = -$100, FV = 0, Compute PV = $496.76Question ID: 19919Consider a 10-year annuity that promises to pay out $10,000 per year; given this is an ordinary annuity and that an investor can earn 10 percent on her money, the future val
9、ue of this annuity, at the end of 10 years, would be:A.$175,312.B.$152,500.C.$110.000.D.$159,374.DAnswer: N=10; I/Y=10; PMT=-10,000; PV=0; CPTFV=$159,374.Question ID: 20981A 5-year, $50,000 loan requires annual end-of-the-year payments of $13,528. What rate of interest is the borrower paying on this
10、 loan (assume annual compounding)?A.11.0%.B.9.5%.C.10.5%.D.9.0%.AN=5; PV=-50,000; FV=0; PMT=13,528; CPT I/Y=11.0%Question ID: 20982The HGM Co. is thinking about taking out a $100,000 loan that is to be paid off in annual (end-of-the-year) payments of $12,042. If the bank agrees to lend the money at
11、8.5 percent, compounded annually, how many years will it take HGM to pay off the loan?A.15.0 years.B.10.9 years.C.8.3 years.D.12.5 years.AI/Y=8.5; PV=-100,000; PMT=12,042; FV=0; CPT N=15.0.Question ID: 20985Given investors require an annual return of 12.5 percent, a perpetual bond (i.e., a bond with
12、 no maturity/due date) that pays $87.50 a year in interest should be valued at:A.$1,093.B.$875.C.$700.D.$70.C87.50/.125=$700.Question ID: 19381Nortal Industries has a preferred stock outstanding that pays (fixed) annual dividends of $3.75 a share. If an investor wants to earn a rate of return of 8.5
13、 percent, how much should he be willing to pay for a share of Nortel preferred stock?A.$37.50.B.$31.88.C.$44.12.D.$42.10.CPV=3.75/.085 = $44.12.Question ID: 20986The preferred shares of AWA Co. are currently trading in the market at $75.00 a share. What rate of return are investors earning on these
14、preferred stock, given they pay (fixed) annual dividends of $6.00 a share?A.8.0%.B.12.5%.C.7.5%.D.6.0%.A6.00/75.00=0.08.Question ID: 20989Given the following cash flow stream: End of YearAnnual Cash Flow1$4,0002$2,0003-0-4-$1,000Using a 10 percent discount rate, the present value of this cash flow s
15、tream is:A.$3,636.B.$2,225.C.$3,415.D.$4,606.DPV(1): N=1; I/Y=10; FV=-4,000; PMT=0; CPT PV=3,636PV(2): N=2; I/Y=10; FV=-2,000, PMT=0; CPT PV=1,653PV(3): 0PV(4): N=4; I/Y=10; FV=1,000; PMT=0; CPT PV=-683Total PV=3,636+1,653+0-683=4,606Question ID: 18503Suppose you are going to deposit $1,000 this yea
16、r, $1,500 next year, and $2,000 the following year in an savings account. How much money will you have in three years if the rate of interest is 10% each year? A.$4,000.00B.$5,346.00C.$5,750.00D.$6,800.00 BFuture value of? $1000 for 3 periods at 10% is 1331Future value of $1500 for 2 periods at 10%
17、is? 1815Future value of $2000 for 1 period at 10% is? 2200Total = $5346n = 3, PV = -$1000, i/yr = 10%, Compute FV = $1331n = 2, PV = -$1500, i/yr = 10%, Compute FV = $1815n = 1, PV = -$2000, i/yr = 10%, Compute FV = $2200Question ID: 19925The BBC Co. is evaluating an investment that promises to gene
18、rate the following annual cash flows:End of YearCash Flows1$5,0002$5,0003$5,0004$5,0005$5,0006-0-7-0-8$2,0009$2,000Given BBC uses an 8 percent discount rate, this investment should be valued at:A.$19,963.B.$22,043.C.$27,027.D.$23,529.BAnswer: PV(1-5): N=5; I/Y=8; PMT=-5,000; FV=0; CPT?PV=19,963PV(6-
19、7): 0PV(8): N=8; I/Y=8; FV=-2,000; PMT=0; CPT?PV=1,080PV(9): N=9; I/Y=8; FV=-2,000; PMT=0; CPT?PV=1,000Total PV=19,963+0+1,080+1,000=22,043.Question ID: 19383Given the following cash flow stream: End of YearAnnual Cash Flow 1 $4,000 2 $2,000 3 0 4 -$1,000 Using a 10 percent discount the present valu
20、e of this cash flow stream is: A.$2,225.B.$4,606.C.$3,415.D.$3,636.BPV(1): N=1; I/Y=10; FV=-4,000; PMT=0; CPT PV=3,636PV(2): N=2; I/Y=10; FV=-2,000, PMT=0; CPT PV=1,653PV(3): 0PV(4): N=4; I/Y=10; FV=1,000; PMT=0; CPT PV=-683 Total PV = 3,636 + 1,653 + 0 - 683 = 4,606 Question ID: 19385What is the ma
21、ximum price an investor should be willing to pay (today) for a 10 year annuity that will generate $500 per quarter (such payments to be made at the end of each quarter), given he wants to earn 12 percent, compounded quarterly?A.$6,440.B.$11,557.C.$5,862.D.$11,300. BUsing a financial calculator: N= 1
22、0x4 = 40; I/Y = 12/4 = 3; PMT= -500; FV=0; CPT PV = 11,557.Question ID: 18508Given: an 11% annual rate paid quarterly; PV = 8000; time is 2 years; compute FV. A.$8,446B.$9,939C.$8,962D.$9,857 BDivide the interest rate by the number of compound periods and multiply the number of years by the number o
23、f compound periods. i=11/4=2.75; n=(2)(4)=8; PV =8000Question ID: 20995A major brokerage house is currently selling an investment product that offers an 8 percent rate of return, compounded monthly. Based on this information, it follows that this investment has:A.a nominal effective rate of 6.67%B.a
24、n effective annual rate of 8.00%C.a periodic interest rate of 0.667%.D.a stated rate of 0.830%.CPeriodic rate = 8.0/12=0.667. Stated rate is 8.0% and effective rate is 8.30%.Question ID: 20996Which of the following statements about stated and effective annual interest rates is/are TRUE?I. The stated
25、 rate adjusts for frequency of compounding.II. The periodic interest rate is used to find the effective annual rate.III. So long as interest is compounded more than once a year, the effective rate will always be more than the stated rate.A.III only.B.II and III only.C.I only.D.I and II only.BStateme
26、nts II and III are true; statement I is wrong since its the effective annual rate that adjusts for frequency of compounding.Question ID: 19387A local bank advertises that it will pay interest at the rate of 4.5 percent, compounded monthly, on regular savings accounts. What is the effective rate of i
27、nterest that the bank is paying on these accounts?A.4.65%.B.4.88%.C.4.59%.D.4.50%. C(1+.045/12)12 - 1 = 1.0459 - 1 = 0.0459.Question ID: 19388Lois Weaver wants to have $1.5 million in a retirement fund when she retires in 30 years. If Weaver can earn a 9 percent rate of return on her investments, ap
28、proximately how much money must she invest at the end of each of the next 30 years in order to reach her goal?A.$11,005.B.$50,000.C.$7,350.D.$28,725. AUsing a financial calculator: N=30; I/Y=9; FV=-1,500,000; PV=0; CPT PMT = 11,004.52.Question ID: 20999The First State Bank is willing to lend $100,00
29、0 for 4 years at a 12 percent rate of interest, with the loan to be amortized in equal semi-annual payments. Given the payments are to be made at the end of each 6-month period, how big will each loan payment be?A.$18,500.B.$16,104.C.$32,925.D.$25,450.BN=4x2=8; I/Y=12/2=6; PV=-100,000; FV=0; CPT PMT
30、=16,103.59.Question ID: 18509Given: $1,000 investment, compounded monthly at 12% find the future value after one year. A.$1,126.83B.$1,120.00C.$1,121.35D.$1,1233.57 ADivide the interest rate by the number of compound periods and multiply the number of years by the number of compound periods. i=12/12
31、=1; n=(1)(12)=12; PV=1000Question ID: 19924Given a preferred stock is trading in the market at $100.00 a share, if the rate of return on this investment is 15 percent, it follows that the stock must be paying (fixed) annual dividends of:A.$5.00 a share.B.$12.50 a share.C.$15.00 a share.D.$7.50 a sha
32、re.CAnswer: $100x.15=$15.00.Question ID: 18488How much will $10,000 grow in 5 years if the annual interest rate is 8%, compounded monthly? A.$14,693.28B.$14,000.00C.$14,898.46D.$14,802.44 CFV(t=5) = $10,000 x (1+.08/12)60 = $14,898.46n = 60 (12*5), PV = -$10,000, i/yr = 8%, Compute FV = $14,898.46Qu
33、estion ID: 18493An 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? A.$496.76B.$400.00C.$800.53D.$396.01 DFirst solve for present value in 3 years: n = 8, PMT =
34、 100, i/yr = 12%, FV = 0, Compute PV = $496.76 Now discount back two years: n = 2, PMT = 0, i/yr = 12%, FV = $496.76, Compute PV = $396.01Question ID: 20006Whats the effective rate of return on an investment that generates a return of 12 percent, compounded quarterly?A.13.33%B.12.55%C.12.00%D.14.34%
35、BAnswer: (1+.12/4)4-1=1.1255-1=.1255.1.B: Statistical Concepts and Market ReturnsQuestion ID: 19684Which of the following statements regarding the terms population and sample is FALSE?A.A sample includes all members of a specified group.B.A descriptive measure of a sample is called a statistic.C.A s
36、ample seeks to describe a population as a whole.D.Observing all members of a population can be expensive or time consuming.AA population includes all members of a specified group. A sample is a portion, or subset of the population of interest.Question ID: 19685Which of the following is an example of
37、 a parameter?A.Sample standard deviation.B.Sample mode.C.Sample mean.D.Population variance.DA parameter is any descriptive measure of a population. The population variance describes a population while the sample standard deviation, sample mean, and sample mode are each descriptive measures of sample
38、s.Question ID: 19686Which measure of scale has a true zero point as the origin?A.Ordinal scale.B.Nominal scale.C.Ratio scale.D.Interval scale.CRatio scales are the strongest level of measurement; they quantify differences in the size of data and have a true zero point as the origin.Question ID: 1968
39、7Fifty mutual funds are ranked according to performance. The five best performing funds are assigned the number 1, while the five worst performing funds are assigned the number 10. This is an example of the:A.ratio scale.B.nominal scale.C.interval scale.D.ordinal scale.DThe ordinal scale of measurem
40、ent categorizes and orders data with respect to some characteristic. In this example, the ordinal scale tells us that a fund ranked “1” performed better than an fund ranked “10,” but it does not tell us anything about the difference in performance.Question ID: 19688Which of the following statements
41、regarding frequency distributions is FALSE? Frequency distributions:A.organize data into overlapping groups.B.work with all types of measurement scales.C.help in the analysis of large amounts of statistical data.D.summarizes data into a small number of intervals.AData in a frequency distribution mus
42、t belong to only one group or interval. Intervals are mutually exclusive and non-overlapping.Question ID: 18880Which of the following best describes a frequency distribution? A frequency distribution is a grouping of:A.selected data into classes so that the number of observations in each of the non-
43、overlapping classes can be seen and tallied.B.raw data into classes so that the number of observations in each of the non-overlapping classes can be seen and tallied.C.independent classes so that they can be seen and tallied.D.dependent classes so that they can be seen and tallied. BBy definition.Question ID: 18878Use the results from the fol