Question

4. A bond has a face value of $1000, a coupon rate of 6%, paid semi-annually, has 23 years to maturity, and the market rate of interest is 7%. What is the value of the bond today?

Answer 1

value of the bond = [present value of annuity factor * semi annual payments] + [present value factor * face value]

here,

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

r = 7% per annum

=>7%*6/12

=>3.5%

=>0.035.

n= 23 years * 2

=>46 periods.

=>[1-(1.035)^(-46)]/0.035

=>0.7945321/0.035

=>22.7009171.

semi annual payments = $1000*6%*6/12=>$30.

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

=>1/(1.035)^46

=>0.20546787

face value =1000

bond value = [22.7009171*30]+[1000*0.20546787]

=>$886.50.