FM for Actuaries

Bonds and Bond Pricing 193
Example 6.3: Find the price of a 18-month zero-coupon bond with redemption
value of $100. The bond is bought to yield 4.24% convertible semiannually.
Solution: It should be noted that the basic price formula (6.1) can be used for
zero-coupon bonds with r =0. We obtain, with i =2.12% and n =3
Example 6.4: Show that
P = Cv n
= 100(1.0212) −3
= $93.90.
P = K + g (C − K),
i
where K = Cv n is the present value of the redemption payment and g = Fr
C
modified coupon rate.
Solution: We start with (6.1) to obtain
P = (Fr)a n⌉
+ Cv n
( ) 1 − v
n
= (Fr) + K
i
( 1 − v
n
)
= Cg + K
i
= g i (C − Cvn )+K
This formula is called the Makeham formula.
is the
= g (C − K)+K. (6.2)
i
6.3 Bond Amortization Schedule
We further develop the basic bond price formula as follows:
P = (Fr)a n⌉
+ Cv n
= (Fr)a n⌉ + C(1 − ia n⌉ )
= C +(Fr− Ci)a n⌉ . (6.3)