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Plain vanilla, two-year interest rate swap

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What would be the swap fixed rate (SFR) for a plain vanilla, two-year interest rate swap, payments every six months beginning 07/01/0X, with the following assumptions/data:
Swap initiation - January 1, 200X
FRA1,0=2.221%; FRA1,1=2.258%; FRA1,2=2.322%; FRA1,3=2.388%;FRA1,4=2.520%;FRA1,5=2.632%
(Read the notation, FRA1,0 as "six-month forward rate from 01/01/0X,FRA1,1 as "six-month forward rate, six months from 01/01/0X, FRA1,2 as "six-month forward rate, one-year from 01/01/0X, etc.)
LIBOR to remain at 2.18%

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Solution Summary

The problem asks for the calculation of swap fixed rate (SFR) for a plain vanilla, two-year interest rate swap. The solution provides a detailed step by step calculation.

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Let the notional Principal be= $10,000,000 (it can be any figure; values of interest payments will change accordingly but SFR will remain the same)
Swap initiation - January 1, 200X
The half yearly payment are made every six months beginning July 1, 0X,
Let the fixed rate payment every half year be F (Colum E)
Floating rate payments are shown in the table below Column C
We also calculate the discount factors
It is customary to discount cash flows in a swap at LIBOR rates which in this case is equal to 2..18%

FRA Floating rate interest payment Fixed rate interest payment "Discount factor for discounting to the beginning of the ...

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