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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 oneyear
maturity, 9.5% for two~year maturity, and 10.5% for threeyear maturity. Let 1' be the oneyear
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 [asHI. 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 oneyear 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) 10.0”) => 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 threeyear 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 = Snack11:13:) + 4' £557 ._; ____;  >
5'”. 'PI II
0
as
c‘
0
“1
.4 Chas) Q’c F.) = (Lens); =5 Hap.
\fthILAnutl (1.9!)(llft)‘ =0. 062:)3= 3  ' o
chm125’ = f ‘3‘”) _ ”0*‘°~"'" ...
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 Fall '08
 Hubscher
 Yield Curve, Zerocoupon bond, coupon bonds, Prof. Rick Gorvett, Actuarial Science Program

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