Question

A bond has a $1,000 par value, a 7% annual coupon, and matures in 19 years. What is the price of this bond (to the nearest dollar) if it has a yield of 12%?

Answer 1

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

here,

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

here,

r=12%=>0.12.

n=19

present value of annuity factor = [1-(1.12)^(-19)]/0.12

=>0.8838932/0.12

=>7.3657767.

coupon payment = $1000*7%=>$70.

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

=>1/(1.12)^19

=>0.11610678.

face value =$1000.

value of the bond = [7.3657767*70] + [0.11610678*1000]

=>515.604369+116.10678

=>$631.71.