This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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*‘°~"'" ...
View Full
Document
 Fall '08
 Hubscher

Click to edit the document details