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Unformatted text preview: UNIVERSITY OF ILLINOIS AT URBANA—CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Prof. Rick Gorvett Fall, 2008 Math 210 Theory of Interest Old Exam 2/FM Problems Yield Curves 1) Yield rates to maturity for zero coupon bonds are currently quoted at 8.5% for one-year maturity, 9.5% for two~year maturity, and 10.5% for three-year maturity. Let 1' be the one-year forward rate for year two implied by current yields of these bonds. Calculate i. o l 1 .3 (A) 85% B 9.5% 835"]. 43‘ > 10.5% —-———-.——> ( ) 115% 4.!" I. ) (E) 12.5% (OJ-'7‘ (May 2005 FMExam, Problem # 10) (Loadlwili =00“); => Llor‘oq'z. “+43, => -P. ﬁ [as-HI. 2) Consider a yield curve deﬁned by the following equation: ik = 0.09 + 0.002]: — 0.00m2 where ik is the annual effective rate of return for zero coupon bonds with maturity of k years. Let j be the one-year effective rate during year 5 that is implied by this yield curve. Calculate j. a t 7, 3 q J“— ‘ M cg = . 032. - _ 0 q o I \ = (C) 6.6% 7 r 1-; .o'ls‘ ,,,,-.(D),,7.5%,, M. . - g3: . . . ’ - . . - (E) 8.2% Wovember 2005 FM Exam, Problem # 6) 6w.)qu {[+er r (tonyllfj) 1-0.0”) => J= 4.05'7. 3) You are given the following term structure of spot interest rates: Spot Term interest g in years) @ 1 5.00% 2 5.75% 3 6.25% 4 6.50% A three-year annuitynimmediate will be issued a year from now with annual payments of 5000. Using the forward rates, calculate the present value of this annuity a year from now. A) 13,094 13,153 (C) 13,296 (D) 13,321 (E) 13,401 Wovember 2005 FM Exam, Problem # 15) o 1 z 3 r t————-—l—-—-——l————l———l T 59o: roan I'OOO IN = Snack-11:13:) + 4' £557 ._; ____;- --- ---> 5'”. 'PI II 0 as c‘ 0 “1 .4 Chas) Q’c F.) = (Lens); =5 Hap. \fthILAnutl (1.9!)(l-l-ft)‘ =0. 062:)3= 3 - ' o chm-125’ = f ‘3‘”) _ ”0*‘°~"'" ...
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