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老师提供的课件，解题过程非常详细：
ANSWERS TO QUESTIONS FOR CHAPTER 2
(Questions are in bold print followed by answers.)
1. A pension fund manager invests $10 million in a debt obligation that promises to pay 7.3% per year for four years. What is the future value of the $10 million?
To determine the future value of any sum of money invested today, we can use the future value equation, which is: Pn = P0 (1 + r)n where n = number of periods, Pn = future value n periods from now (in dollars), P0 = original principal (in dollars) and r = interest rate per period (in decimal form). Inserting in our values, we have: P4 = $10,000,000(1.073)4 = $10,000,000(1.325558466) = $13,255,584.66.
2. Suppose that a life insurance company has guaranteed a payment of $14 million to a pension fund 4.5 years from now. If the life insurance company receives a premium of $10.4 million from the pension fund and can invest the entire premium for 4.5 years at an annual interest rate of 6.25%, will it have sufficient funds from this investment to meet the $14 million obligation?
To determine the future value of any sum of money invested today, we can use the future value equation, which is: Pn = P0 (1 + r)n where n = number of periods, Pn = future value n periods from now (in dollars), P0 = original principal (in dollars)and r = interest rate per period (in decimal form). Inserting in our values, we have: P4.5 = $10,400,000(1.0625)4.5 = $10,400,000(1.313651676) = $13,661,977.43. Thus, it will be short $13,661,977.43 – $14,000,000 = –$338,022.57.
3. Answer the following questions.
(a) The portfolio manager of a tax-exempt fund is considering investing $500,000 in a debt instrument that pays an annual interest rate of 5.7% for four years. At the end of four years, the portfolio manager plans to reinvest the proceeds for three more years and expects that for the three-year period, an annual interest rate of 7.2% can be earned. What is the future value of this investment?
At the end of year four, the portfolio manager’s amount is given by: Pn = P0 (1 + r)n. Inserting in our values, we have P4 = $500,000(1.057)4 = $500,000(1.248245382) = $624,122.66. In three more years at the end of year seven, the manager amount is given by:
P7 = P4(1 + r)3. Inserting in our values, we have: P7 = $624,122.66(1.072)3 = $624,122.66(1.231925248) = $768,872.47.
(b) Suppose that the portfolio manager in Question 3, part a, has the opportunity to invest the $500,000 for seven years in a debt obligation that promises to pay an annual interest rate of 6.1% compounded semiannually. Is this investment alternative more attractive than the one in Question 3, part a?
At the end of year seven, the portfolio manager’s amount is given by the following equation, which adjusts for semiannual compounding. We have: Pn = P0(1 + r/2)2(n). Inserting in our values, we have P7 = $500,000(1 + 0.061/2)2(7) = $500,000(1.0305)14 = $500,000(1.522901960) = $761,450.98. Thus, this investment alternative is not more attractive. It is less by the amount of $761,450.98 – $768,872.47 = –$7,421.49.
4. Suppose that a portfolio manager purchases $10 million of par value of an eight-year bond that has a coupon rate of 7% and pays interest once per year. The first annual coupon payment will be made one year from now. How much will the portfolio manager have if she (1) holds the bond until it matures eight years from now, and (2) can reinvest all the annual interest payments at an annual interest rate of 6.2%?
At the end of year eight, the portfolio manager’s amount is given by the following equation, which adjusts for annual compounding.
We have:
where A = coupon rate times par value. Inserting in our values, we have:
+ $10,000,000 = $700,000[9.9688005] + $10,000,000 = $6,978,160.38 + $10,000,000 = $16,978,160.38.
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