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old6 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial...

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Unformatted text preview: UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 210 Prof. Rick Gorvett Theory of Interest Fall, 2008 Old Exam 2/FM Problems 2m (1) Calculate the Macaulay duration of an eight-year 100 par value bond with 10% annual coupons and an effective rate of interest equal to 8%. MM} = Zt'ID-V" +loov’zf') _ IoCIaEE-I-J’oov A 4 - (B)5 2 WV": + 100v? “3‘05; +Ioov )7 = 5'. ‘0 ‘l (E) 8 ' fWovember 2005 FM Exam, Problem # 2) (2) A bond will pay a coupon of 100 at the end of each of the next three years and will pay the face value of 1000 at the end of the three-year period. The bond’s duration (Macaulay duration) when valued using an annual effective interest rate of 20% is X. Calculate X. 3 mM’ +r°°CW‘+ 19.9.) (A 2.61 _ . . . _ .. ‘2-70 “Mb " loov' Hoov" + Hobo? (C) 2.77 (D) 2.39 = 2 _ n o (E) 3-00 M (May 2005 FM Exam, Problem # 3) (3) John purchased three bonds to form a portfolio as follows: Bond A has semi-annual coupons at 4%, a duration of 21.46 years, and was purchased for 980. Bond B is a 15-year bond with a duration of 12.35 years and was purchased for 1015. Bond C has a duration of 16.67 years and was purchased for 1000. Calculate the duration of the portfolio at the time of purchase. (A)16.62years WOCU-‘f‘l + totrflmsrl 4- looo(lé.t'\l W (B)16.67 years ‘.but“. ': C 16.72years ‘ifo +IOIF+IODO @) 6.77 years W 16.82 years .. (May 2005 FM Exam, Problem # 6) .. l 6. it”) ...
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