 Solution

Each floating payment in the interest rate swap has initial value $P_0(t-1)-P_0(t)$ by the previous replication. Their sum telescopes to $1-P_0(T)$. The fixed leg pays $s$ at each of the same dates, so its initial value is $s{\sum }_{t=1}^T{P}_0(t)$. Consequently the par swap rate isThe denominator is positive. This is for unit accrual periods and the printed floating-minus-fixed payments. No extra exchange of principal occurs in the contract; the principal-like terms appear only because the floating-leg replication telescopes.