单选题 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.

单选题 The semi - annual effective rate is :

A.9.20%.
B.9.00%.
C. 10.25%.

【正确答案】 A

【答案解析】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%.

单选题 An investment offers $100 per year forever. If Peter Wallace's 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.

单选题 The quarterly effective rate is:

A.9.31%.
B.9.00%.
C.9.20%.

【正确答案】 A

【答案解析】First, we need to calculate the periodic rate, or 0.09/4=0.0225.
Then, the effective annual rate = (1+0.0225)⁴-1=0.09308, or 9.31%.

单选题 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 investor's investments ?

Investment	Invested Amount	Return(%)
A	10000	12
B	10000	14
C	10000	9
D	20000	13
E	20000	7

A. 11.64 10.78
B. 1.64 10.97
C. 11.00 10.97

【正确答案】 C

【答案解析】Arithmetic Mean: 12 + 14 +9 + 13 +7 =55; 55/5 = 11 ; Geometric Mean: [*]

单选题 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. $ 234422.
B. $ 274422.
C. $ 272977.

【正确答案】 B

【答案解析】This is an annuity due so set your calculator to the BGN mode. N=15; I/Y=14.5; PMT=-40000; FV=0; CPT→PV=274422.50. Switch back to END mode.

单选题 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 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 data set by examining a smaller sample.

【正确答案】 C

【答案解析】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.

单选题 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 due.
C. The present value of the ordinary annuity is less than an annuity due.

【正确答案】 C

【答案解析】With a positive interest rate, 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 annuity is discounted one period more.

单选题 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 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.

【正确答案】 A

【答案解析】A frequency distribution is a tabular presentation of statistical data that aids the analysis of large data sets.

单选题 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 is 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%.

【正确答案】 B

【答案解析】Joint probability is the probability that both events, in this case the economy 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.

单选题 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 of return (IRR) for this investment is closest to.

A. 15%.
B. 30%.
C. 25%.

【正确答案】 C

【答案解析】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 = 0
One way to compute 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%.

单选题 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 this account is.

A. 9.01%.
B.4.65%.
C. 8.24%.

单选题 The financial manager at Kyser Jones is considering two mutually exclusive projects with the following projected cash flows:

Projected Cash Flows
Year	Project M	Project Z
0	-$60000	-$60000
1	22500	0
2	22500	0
3	22500	0
4	22500	111000

If Kyser 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.

【正确答案】 B

【答案解析】Since the projects are mutually exclusive, only one of the projects may be choosen. Project Z has the higher NPV. On the exam, always use NPV for choosing between nutually exclusive projects.

Cash Flow Input Values
	Project M	Project Z
CF0	-60000	-60000
CF1	22500	0
F1	4	3
CF2		111000
F2		1
Output Values
	Project M	Project Z
NPV	$9805	$13119
IRR	18.45%	16.62%

单选题 A distribution that is more peaked than normal is:

A. skewed.
B. platykurtic.
C. leptokurtic.

【正确答案】 C

【答案解析】A distribution that is more peaked than normal is leptokurtic. A distribution that is flatter than normal is platykurtic.

单选题 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.

【正确答案】 A

【答案解析】The expected values are: E(X) =(0.3×2)+(0.4×6)+(0.3×10)=6 and E(Y) =(0.3×10.0)+(0.4×2.5)+(0.3×0.0)=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.

单选题 For a stock, which of the following is NOT a random variable?

A. Its most recent closing price.
B. Its P/E ratio.
C. Its stock symbol.

【正确答案】 C

【答案解析】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 like the number of letters in the symbol. The symbol itself cannot be a random variable.

单选题 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%.
B. 10.0%.
C. 12.5%.

【正确答案】 C

【答案解析】The holding period return (HPR) is calculated as follows:
HPR = (P_t - P_t-1 + D_t)/P_t
where :
P_t = price per share at the end of time period t
D_t = cash distributions received during time period t.
Here, HPR = (850-800+50)/800=0.1250, or 12.50%.

单选题 Use the results from the following survey of 500 firms to answer the question.

Number of Employees	Frequency
300 up to 400	40
400 up to 500	62
500 up to 600	78
600 up to 700	101
700 up to 800	131
800 up to 900	88

The cumulative relative frequency of the second interval (400 to 500) is:

A. 20.4%.
B. 10.2%.
C. 36.0%.

单选题 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.

【正确答案】 C

【答案解析】A positive covariance indicates a positive linear relationship but nothing else. The magnitude of the covariance by itself is not informative with respect to the strength of the relationship.

单选题 If the outcome of event A is not affected by event B, then events A and B are said to be:

A. mutually exclusive.
B. statistically independent.
C. collectively exhaustive.

【正确答案】 B

【答案解析】If the outcome of one event does not influence the outcome of another, then the events are independent.

单选题 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 value of the car for 36 months at 8 percent annual interest, his monthly payments will be:

A. $289.
B.$413.
C. $376.

单选题 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 four annual withdrawals 10 - years from today? The expected rate of return is 8 percent.

A. $ 30683.
B. $ 66243.
C. $ 33138.

【正确答案】 C

【答案解析】Two steps. 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 =0. 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=20000; CPT→PV=$66242.54. Second, find the present value of this single sum: N=9; I/Y=8; FV=66242.54; PMT=0; CPT→PV=33137.76.

单选题 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(n).

A. opportunity cost.
B. discount rate.
C. required rate of return.

【正确答案】 B

【答案解析】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.

单选题 Consider a 10 - year annuity that promises to pay out $10000 per year; 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.

单选题 A joint probability of A and B must always be:

A. less than or equal to the conditional 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.

【正确答案】 A

【答案解析】By the formula for joint probability: P(AB)=P(A|B)×P(B), since P(B)≤1, then P(AB)≤P(A|B). None of the other choices must hold.

单选题 If the odds against an event occurring are twelve to one, what is the probability that it will occur?

A. 0.0769.
B. 0.0833.
C. 0.9167.

【正确答案】 A

【答案解析】If the probability against the event occurring is twelve to one, this means that in thirteen occurrences of the event, it is expected that it will occur once and not occur twelve times. The probability that the event will occur is then: 1/13 =0.0769.