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%?
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.
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