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Let C = the coupon rate. Then the bond pricing equation is:
C($1000)/(1+.075)+ C($1000)/(1+.075)^2 + C($1000)/(1+.075)^3 + … C($1000)/(1+.075)^12
For which I do not know of any algebraic solution.
However, there are two things to note:
1. If this were a multiple choice question, we would know that C > 7.5 = YTM because the bond is selling at a premium (P = $1045 > par = $1,000).
2. We can set this up as a present value problem in Excel and use “Goal Seek” to find C....
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