First payment of floating rate swap

[h21]

I get confused, why is the first payment for floating rate is the same for the fixed payment when we are calculating their values?

 

[S2000magician]

I have no idea what you’re asking.
In a plain vanilla interest rate swap, every payment is the same: the fixed-rate payer pays the fixed rate, and the floating rate payer pays the floating rate.

 

[h21]

sorry
so we know 4 rate and 4 discount factors for a payment, we can calculate the fixed rate
I mean when we calculate the floating leg of the swap, we know the discount factor and par payment, we need the first payment to calculate the floating value, why is the floating payment the same as the first of the 4 rate provided?
the question is based on question 1.b of exercise of reading 49 on EOC

 

[krokodilizm]

1/(1+r)^t = (1+r)^-t and it is the general form for discounting any cash flow.
(1-Zn)/(Z1+Z2+Zn) is a shortcut formula for calculating the fixed rate in a swap. It is derived in a rather complicated way so you better just memorize it.
Therefore, these two are not the same thing and should not be compared.