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北美精算师2001年11月真题Course2（第三节课）

来源：高顿网校 2014-08-25

　　下面的北美精算师2001年11月真题Course2（第三节课），请相关备战精算师人士赶快消化掉。
　　21. In a perfectly competitive market, the market supply and demand functions are:

　　Supply: P = 4Q

　　Demand: P = 100 . Q

　　where P is price and Q is quantity.

　　The total variable cost function (TVC) for an individual firm is:

　　TVC = 76q + q2

　　where q is the quantity produced by the firm.

　　What is the output for the firm?

　　(A) 0

　　(B) 2

　　(C) 8

　　(D) 20

　　(E) 38

　　Course 2, November 2001 23

　　22. A firm.s market value balance sheet is as follows:

　　Asset Value 500 Debt 200

　　Equity 300

　　Firm Value 500 Firm Value 500

　　The risk-free rate of interest is 3.5%, bequity is 1.2, bdebt is 0.2, and the return on the

　　market portfolio is 14.4% .

　　Calculate the company.s cost of capital.

　　(A) 5.7%

　　(B) 7.2%

　　(C) 10.0%

　　(D) 12.2%

　　(E) 16.6%

　　Course 2, November 2001 24

　　23. Suppose purchasing power parity exists between the United States and the United

　　Kingdom. The current inflation rates are 3.0% in the U.S. and 5.0% in the U.K.

　　The current nominal exchange rate is 2.0 dollars per pound.

　　What is the expected exchange rate one year from now?

　　(A) 1.20

　　(B) 1.96

　　(C) 2.00

　　(D) 2.04

　　(E) 3.33

　　Course 2, November 2001 25

　　24. David can receive one of the following two payment streams:

　　(i) 100 at time 0, 200 at time n, and 300 at time 2n

　　(ii) 600 at time 10

　　At an annual effective interest rate of i, the present values of the two streams are equal.

　　Given vn = 0.75941, determine i .

　　(A) 3.5%

　　(B) 4.0%

　　(C) 4.5%

　　(D) 5.0%

　　(E) 5.5%

　　Course 2, November 2001 26

　　25. A stock currently has a price of 45.00 and pays no dividends. One year from now, there

　　is a 50% probability that the price of the stock will be 30.00 and 50% that it will be

　　greater than 40.00 .

　　The risk-free rate is 4% .

　　Calculate the price of a one-year European call option with an exercise price of 40.00 .

　　(A) 4.81

　　(B) 6.35

　　(C) 9.81

　　(D) 10.00

　　(E) 11.35

　　Course 2, November 2001 27

　　26. Joe’s budget line is defined by the equation y = .0.5x + 18, where y is the quantity

　　of meat and x is the quantity of bread.

　　If Joe’s income increases, what will happen to the slope and the y-intercept of his

　　budget line?

　　(A) Both the slope and the y-intercept will increase.

　　(B) The slope will increase while the y-intercept will remain unchanged.

　　(C) The slope will decrease while the y-intercept will remain unchanged.

　　(D) The slope will remain unchanged while the y-intercept will decrease.

　　(E) The slope will remain unchanged while the y-intercept will increase.

　　Course 2, November 2001 28

　　27. A man turns 40 today and wishes to provide supplemental retirement income of 3000 at

　　the beginning of each month starting on his 65th birthday. Starting today, he makes

　　monthly contributions of X to a fund for 25 years. The fund earns a nominal rate of 8%

　　compounded monthly.

　　Each 1000 will provide for 9.65 of income at the beginning of each month starting on his

　　65th birthday until the end of his life.

　　Calculate X.

　　(A) 324.73

　　(B) 326.89

　　(C) 328.12

　　(D) 355.45

　　(E) 450.65

　　Course 2, November 2001 29

　　28. Payments are made to an account at a continuous rate of (8k + tk), where ere 0≤t≤10 .

　　Interest is credited at a force of interest δt = 1

　　8 + t

　　.

　　After 10 years, the account is worth 20,000 .

　　Calculate k .

　　(A) 111

　　(B) 116

　　(C) 121

　　(D) 126

　　(E) 131

　　Course 2, November 2001 30

　　29. Suppose a consumer.s income increases and, at the same time, the price of X decreases.

　　Further suppose that in the new situation the consumer purchases less X than before.

　　Which of the following must be true?

　　(A) X is a normal good.

　　(B) X is an inferior good.

　　(C) X is a Giffen good.

　　(D) X is a luxury good.

　　(E) X is a good for which the compensated demand curve

　　is steeper than the uncompensated demand curve.

　　Course 2, November 2001 31

　　30. Nate intends to invest in two different stocks, X and Y .

　　Stock X has an expected return of 10% and a standard deviation of Z .

　　Stock Y has an expected return of 20% and a standard deviation of 1.5Z .

　　After investing in both stocks, the expected return on Nate.s two-stock portfolio is 12%

　　and the standard deviation is Z .

　　Calculate the correlation between the returns on Stocks X and Y .

　　(A) 0.50

　　(B) 0.53

　　(C) 0.56

　　(D) 0.60

　　(E) 0.63

　　Course 2, November 2001 32
　　我虽然不同意你说的话，但是我维护你说话的权利。——高顿网校生活感悟

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