Question

An 8% bond pays semi-annually and matures in 10 years. You require 6% for bonds with this bond's risk characteristics. What price would you expect to pay for the bond?

Answer 1

price to be paid for the bond = [present value of annuity * interest payment ] + [present value factor * face value]

here,

present value of annuity = [1 - (1+r)^(-n)]/r

r = 6% required rate per annum =>6%*6/12 =>3% for semi annual period =>0.03.

n = 10 years * 2 semi annual periods

=>20 .

present value of annuity = [1-(1.03)^(-20)]/0.03

=>[0.4463243/0.03]

=>14.8774767.

interest payment = $1,000 face value (assumed as default value) * 8% * 6/12 =>$40.

present value factor = 1/(1+r)^n

=>1/(1.03)^20

=>0.55367575.

face value =$1000

now,

payment to be made for the bond = [14.8774767*$40]+[0.55367575*$1000]

=>595.099068+553.67575

=>$1,148.77.