Question

What is the market price of a $1,000, 8 percent bond - paying interest semi-annually - if comparable market interest rates drop to 6 percent and the bond matures in 15 years?

Is the answer $1,194?

Answer 1

bond price = [present value of annuity * interest payment] + [present value factor *face value]

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

here,

r= 6% per annum

=>3% for six months

=>0.03.

n = 15 years * 2 semi annual periods

=>30.

=>[1-(1.03)^(-30)]/0.03

=>19.60044

interest payment = $1000 * 8%*6/12 =>$40.

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

=>1/(1.03)^30

=>0.41198676

face value = 1000

market price = [19.60044*40]+[0.41198676*1000]

=>784.0176+411.98676

=>$1,196.