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Luke enters into a three-year interest rate swap to receive a fixed rate and pay a variable rate based on future 1-year LIBOR rates. The settlement occurs at the end of every year. The notional amount is 1,000 for year 1, 800 for year 2, and 600 for year 3. tt stst 1 4% 2 5% 3 6% 4 7% 5 8% Determine the net swap payment made at the end of the first year.

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danialamin

Answer:

The net swap payment made is $49.

Explanation:

In order to find the solution the values are used which are as follows:

The Value of interest in each year is calcuated as follows

[tex]Interest=Interest\ Rate\%\times Amount[/tex]

The values of interest rate and amount for 3 years are as follows:

  • Interest rate for year 1 is 4% for an amount of 1000
  • Interest rate for year 2 is 5% for the amount of 1800
  • Interest rate for the year 3 is 6% for the amount of 800.

These values are calculated as follows:

[tex]Interest_1=4\%\times 1000\\Interest_1=40[/tex]

Similarly

[tex]Interest_2=5\%\times 1800\\Interest_2=90[/tex]

Also

[tex]Interest_3=6\%\times 800\\Interest_3=48[/tex]

So the total interest is

[tex]Interest_T=Interest_1+Interest_2+Interest_3\\Interest_T=40+90+48\\Interest_T=178[/tex]

The total amount is given as

[tex]Amount_T=Amount_1+Amount_2+Amount_3\\Amount_T=1000+1800+800\\Amount_T=3600[/tex]

Fixed rate is given as

[tex]\dfrac{Interest_T}{Amount_T}\\=\dfrac{178}{3600}\\\\=0.049\ or\ 4.9\%[/tex]

Now for the swap payment made at the end of first year is

[tex]Amount_{1st swap}=Fixed Rate\times Amount_1\\Amount_{1st swap}=4.9\%\times 1000\\Amount_{1st swap}=$49[/tex]

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