Let's say that Jim buys a bond whose face value is 100$ and has a 4.75% coupon, with coupon payments given annually, that matures in 5 years. Jim buys this bond today for 103.05$.
Letting x represent the discount rate, I know that
4.75 * (1 - (1+x)^-5) / x + 100 * (1+x)^-5 = 103.05
and (assuming Jim made a good trade) Wolfram Alpha tells me that the discount rate is at most .04064.
My question is: how did Jim know that the discount rate was at most this amount?
Edit: In response to Max's answer, I'm not looking for the calculations, instead, I'm more looking for the reasoning that Jim uses to say that "I should value this bond as if the discount rate was 4.064% ." Is he able to look this number up somewhere?