Floating or fixed payment-based on term structure of a swap

[h21]

hi all, i am confused by what is fixed and what is floating based on a term structure.
When provided a term structure, i believe what it means it is the term for fixed payment structure, however, when we are calculating the floating payment, this is what the answer give us-use the first interest rate in the fixed structure to calculate the floating paymen, specifically i am talking about question 9 of exercise in reading 50
The first floating payment is (based on the 180-day rate of 4.20 percent in effect at the time the swap is initiated) $50,000,000(0.0420 × 180/360) = $1,050,000.
maybe I missed some part, can someone break down to me why floating structure is the same as fixed term in the first payment again?

 

[krokodilizm]

If you signed a swap agreement to pay fixed you don’t care how term structure changes. You will pay only at one predetermined rate.
If you agreed to pay floating then at every payment date, i.e. every six month, you will pay at the current rates prevailing at that date. So you are at the mercy of the market. If rates go up you will pay more and vice versa.

 

[h21]

and at the first period, the rate is the same as fixed, which is 4.2

 

[S2000magician]

The short answer is: no.
Take a look at the article I wrote on pricing a plain vanilla interest rate swap: http://financialexamhelp123.com/pricing-plain-vanilla-interest-rate-swaps/
The swap fixed rate is 6.2566%, but the 6-month LIBOR rate is 3%. So at the first payment date the fixed payer will pay 3.1283% of the notional amount and the floating payer will pay 1.5% or the notional.
Of course these payments are netted, so fixed payer will pay 1.6283% (= 3.1283% − 1.5%) of the notional.