The coupon rate=8.781% as bonds on the market making annual payments, with 14 years to maturity, a par value of $1,000, and a current price of $1,108.60.
The price at the moment is stated as;
Current price=C×{1-(1/(1+r)^n)}/r+{F.V/(1+r)^n}
where;
C=current price
r=annual yield to maturity rate
n=number of years to maturity
F.V=face value
In our case;
C=$1,108.60
r=7.5%=7.5/100=0.075
n=14 years
F.V=$1,000
replacing;
1,108.60=C×{1-(1/(1+0.075)^14)}/0.075+{1,000/(1+0.075)^14}
1,108.60=C×{1-1/(1.075^14)}/0.075+{1,000/1.075^14}
1,108.60=(C×0.637/0.075)+363.313
1,108.60-363.313=8.48915 C
C=$87.81
But;
Annual coupon payments=coupon rate×face value
where;
annual coupon payments=$87.81
coupon rate=R%=(1/100)R=0.01 R
face value=$1,000
replacing;
87.81=0.01 R×1,000
R=87.81/(0.01×1,000)=8.781% = 8.781
Thus, The coupon rate=8.781%
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