Question

On the 15th of May 2012 you enter a Forward Rate Agreement (FRA) to borrow on the 15th of September 2012 $1’000’000 for 7 months at a fixed annualized interest rate of 5% (for a FRA with a contract length of 7 months the compounding frequency is 12 7 -times c.p.a.). What is the value of the FRA for you as a borrower on the 15th 3 of August 2012 if (on the 15th of August) the 1-month spot rate is 3% (semi-annual compounded) and the 8-month spot rate is 5% (monthly compounded)?

Answer 1

1- Month Spot rate (effective) = ((1+0.03/2)^2-1)/12 = 0.2529%

8 - Month Spot Rate(effective) = ((1+0.05/12)^12-1)*8/12 = 3.3750%

7- Month Forward Rate(efective) = (1+3.3750%)/(1+0.2529%)-1 = 3.1142%

effective Rate for 7 month as per the FRA = ((1+0.05/12)^12-1)*7/12 = 2.9844%

Savings Due to FRA = 1000000*(3.1142%-2.9844%) = $1,298

Present Value of this $1298, this 1298 saving will happen 8-month from the 15th august 2012, so we need to figure out the Present value:- please remember we have already calculated the 8-Month Effective Rate as GIven Above = 3.3750%

Value of FRA =1298/(1+3.3750%) = $1,255.623

I hope my efforts will be fruitful to you

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