If the bond is held until maturity, the bond will pay $5 as interest and $100 par value for the matured bond. For the $99.44 investment, the bond investor will receive $105 and therefore the yield to maturity is 5.56 / 99.44 for 5.59% in the one year time period. Then continuing by trial and error, a bond gain of 5.53 divided by a bond price of 99.47 produces a yield to maturity of 5.56%. Also, the bond gain and the bond price add up to 105.