What is the price per 1000 of face value of a 9 year 4 coupo

What is the price (per $1,000 of face value) of a 9 year 4% coupon-bond issued
by the U.S. Treasury? You may assume that the discount rate is 6%.

Solution

Solution = Calculation of Price of bond

Price of bond = [(P*r)*PVIF(i,n)] + [(P)*PVIFA(i,n]

Here, P = Face value of bond i.e. $1000

r = Coupon rate i.e. 4%

n = Maturity Period i.e. 9 years

i = Discount rate i.e. 6%

PVIF =[1/1+i]ⁿ = [1/1.06]⁹ = 6.8017

PVIFA =[1/1.06]^{9th Year} = 0.5919

Price of bond = ($1000*4%)*6.8017 + ($1000*0.5919)

Price of the bond = $272.068 + $591.9

Price of the bond = $864 (rounded off)