Krzys’ Ostaszewski, http://www.math.ilstu.edu/krzysio/, Exercise 109, 6/16/2007
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May 2005 Casualty Actuarial Society Course 8 Examination, Problem No. 27(b)
(multiple choice answers added)
The yield-to-maturity on one-year zero-coupon bond is currently 7%. The yield-tomaturity on two-year zero-coupon bond is currently 8%. The Treasury plans to issue a
two-year maturity coupon bond, paying coupons once per year with a coupon rate of 9%.
The face value of the bond is $100. Calculate the two-year coupon bond’s yield to
maturity.
A. 7.99%
B. 7.96%
C. 7.93%
D. 7.91%
E. 7.88%
Solution.
The price of the two-year coupon bond, based on the spot interest rates, is equal to
$9
$109
+
! $101.86.
1.07 1.08 2
Its yield-to-maturity i (annual effective rate) must satisfy the equation
$9
$109
+
= $101.86.
1 + i (1 + i )2
This gives i ! 7.956942%.
Answer B.
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