For the second year, you've already amortized $6 of your regular bond premium, so the unamortized bond premium is $80 minus $6, or $74. Multiply $1,074 by 5% to get $53.70, subtract it from $60, and you can see that you'll amortize $6.30 in the second year, leaving you with $67.70 in unamortized bond premium.
By amortizing your bond premium, you can get tax benefits during the course of owning the bond, rather than having to wait until you sell it or until it matures. The method requires that you keep track of your unamortized bond premium, but that's a small price to pay for tax savings.