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a semi-annual coupon bond as a par value of $1,000 and matures in ten years because its semi-annual there are 20 periods we want to know what the coupon rate is given the price and the yield to maturity today lets write down what we do know we know that the bond will pay us the par value of $1,000 in 20 periods we know that it sells today for eight hundred and eighty seven dollars so thats the present value of all of the future cash flows from owning this bond were told that has a yield to maturity of ten point nine percent because it is semiannual the periodic rate would be half of ten point nine percent which would be five point four five percent and we see that the one piece of information that is unknown is what this six-month bond payment will be and once you realize that this is the thing that is unknown I think you can realize how we can find the coupon rate its by finding out what this payment is and then we just use the simple formula for coupon rate so lets find out wh