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Review_Final - ACF329 Practice Problems for Final Exam...

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ACF329 Practice Problems for Final Exam Warning: this is not a sample test, and it only includes material not covered in the midterms. Name: Instructions: You should use one of the SOA approved calculators on this worksheet. These problems are from the sample Exam FM problems you can access from the Society of Actu- aries webpages. Some of them are slightly modified. Make sure you know how to use your calculator. I will not answer any questions during the exam on how to use the calculator. For example, “BGN” versus “END”; although it’s possible to calculate all annuity symbols with just one of them, it may be more convenient to be able to use both. 1. Important! This one item is not a problem, but a written correction of an error I made during class. One of the formulas from Section 3.9 (Annuities with payments in arithmetic progression) was presented incorrectly. In class, I wrote ( I P,Q ¨ a ) i = P ¨ a i + Q d ¨ a i = P d + Q d 2 . That was incorrect! The correct formula is ( I P,Q ¨ a ) i = P ¨ a i + Q d a i = P d + Q id I apologize for any confusion I may have caused by this error. I have never used this formula to solve any problems in class so hopefully only a minor correction is needed in your notes. 2. You are given the following information with respect to a bond: Par amount: 1000 Term to maturity: 3 years annual coupon rate: 6% payable annually Term Annual Spot Interest Rates 1 7% 2 8% 3 9% Calculate the value of the bond and the annual effective yield rate for the bond if the bond is sold at a price equal to its value. ACF329 Spring 2011 Harper
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3. A 1000 bond with semi-annual coupons at i (2) = 6% matures at par on October 15, 2020. The bond is purchased on June 28, 2005 to yield the investor i (2) = 7%. Calculate the purchase price to the nearest whole number. Assume simple interest between bond coupon dates. Also, assume that there are 183 days between coupon dates, and note that: Date Day of the Year April 15 105 June 28 179 October 15 288 4. The current price of an annual coupon bond is 100. The derivative of the price of the bond with respect to the yield to maturity is - 700. The yield to maturity is an annual effective rate of 8%. Calculate the duration of the bond. 5. Calculate the duration of a common stock that pays dividends at the end of each year into perpetuity. Assume that the dividend is constant, and that the effective rate of interest is 10%. 6. Calculate the duration of a common stock that pays dividends at the end of each year into perpetuity. Assume that the dividend increases by 2% each year and that the effective rate of interest is 5%.
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