Answer: The coupon rate on the bonds is 7.50%.
The current price of a bond is nothing but the discounted value of the coupon payments and the face value at the yield or YTM.
Hence, mathematically the bond's price is given by the formula:
[tex]\mathbf{CMP_{bond} = C*\left ( \frac{1-(1+r)^{-n}}{r} \right) + \frac{FV}{(1+r)^{n}}}[/tex]
where,
CMP = Current Market Price of the bond
C = Coupon in dollars
r = YTM
n = number of years to maturity
FV = Face Value
Substituting the values in the equation above we get,
[tex]967 = C*\left ( \frac{1-(1.079)^{-14}}{0.079} \right) + \frac{1000}{(1.079)^{14}}[/tex]
Solving further we get,
[tex]967 = C*8.292338915 + \frac{1000}{2.899347199}[/tex]
[tex]967 = C*8.292338915 + 344.9052257 [/tex]
[tex]622.0947743 = C*8.292338915[/tex]
\mathbf{C = 75.02042315}
Since the dollar value of coupons is $75.02042315, we can calculate the coupon rate on the bonds as:
[tex]\mathbf{Coupon rate = \frac{Coupon}{Face Value}*100}[/tex]
[tex]Coupon rate = \frac{75.02042315}{1000}*100[/tex]
[tex]Coupon rate = 0.075020423*100[/tex]
[tex]\mathbf{Coupon rate = 7.502042%}[/tex]
