OLG - Government Budget Constraint
The interest component is already included. It was just their way of writing out the budget constraint that confused me. If anyone is interested:

$\frac{B_{t-1}}{p_{t}} - \frac{B_{t}}{(1+i_{t})p_{t}} = \frac{i_{t}}{(1+i_{t})}\frac{B_{t}}{p_{t}} - \frac{B_{t}}{p_{t}} + \frac{B_{t-1}}{p_{t}}$. This is simply the interest on existing debt and the face value of existing debt (on the expenditure side). And real bond issuance on the income side. Simple rearranging and you have it.