FM for Actuaries

Bonds and Bond Pricing 211
6.23 Show that
dP
di = − C [
]
n
1+i (1 + i) n + g(Ia) n⌉
and that
d 2 P
di 2 > 0.
6.24 A $1,000 par value 16-year bond with m coupons per annum has a price of
$910.63. If the total write-up value in the book value of the bond in the first
8 years is $54 and the yield rate of the bond is 5.0945% effective per annum,
find the redemption value of the bond.
6.25 One method of calculating the write-up or write-down of the book value of a
bond is the straight-line method. This method is used for taxation purposes
in the US for bonds purchased at premium and issued before the Tax Reform
Act 1986. Under the straight-line method, the book value decreases from the
purchase price to the redemption value linearly over the life of the bond. For
the bond considered in Table 6.1, construct the bond amortization schedule
using the straight-line method. Is this method consistent with the theory of
compound interest or simple interest?
6.26 A $100 par value 20-year callable bond paying 5.5% coupons annually has a
call protection period of 10 years. The bond is redeemable
(a) at the end of the 11th to the 15th year, at 104%,
(b) at the end of the 16th to the 20th year, at par.
Find the price of the bond if the yield rate of the bond is not less than 5.3%.
6.27 For a $1,000 par value 10-year bond with annual coupons, you are given the
following information:
Time Coupon Effective Amortized amount Book
(in year) payment interest earned of premium value
.
.
5 54.099
6 54.945
7 55.842
.
.
Find the sum of the premiums or discounts in the last 2 years of the term of
the bond.