Unformatted text preview: UNIVERSITY OF ILLINOIS AT URBANACHAMPAIGN
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 eightyear 100 par value bond with 10% annual
coupons and an effective rate of interest equal to 8%. MM} = Zt'IDV" +loov’zf') _ IoCIaEEIJ’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 threeyear 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 _ . . . _ .. ‘270 “Mb " loov' Hoov" + Hobo? (C) 2.77 (D) 2.39 = 2 _ n o (E) 300 M (May 2005 FM Exam, Problem # 3)
(3) John purchased three bonds to form a portfolio as follows: Bond A has semiannual coupons at 4%, a duration of 21.46 years,
and was purchased for 980. Bond B is a 15year 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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 Fall '08
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