In valuing a fixed for floating interest rate swap after initiation, how is the new rate to be accounted for?

Curriculum applies all the present value factors of remaining maturity, schweser only takes the current quarter present value, Wiley has no example on this altogether.

Exactly, anyway I only want to know how much should one discount a (new) floating rate, only for one period or all of the remaining maturity of the contract? As I see it being differently done in Schweser than curriculum.