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I have some trouble to understand on valuing the floating side of a swap. In my book, the value of floating side at the time t is;

$$ P(t,T_0) - P(t,T_n) $$

Where $$ P(t,T_n)$$ denotes the value of zero coupon bond at time t which payoff $1 at the maturity. However, there are no additional explanation about this and I think that I'm missing some point at this swap valuation process. I think that floating side should pay floating rate at every reset moment, so above formula is not intuitive for me.

May I ask what is missing on this valuation?

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