Problem:

On the 15th of May 2013 you enter a Forward Rate Agreement (FRA) to borrow on the 15th of September 2013 $1,000,000 for 8 months at a fixed annualized interest rate of 5% (for a FRA with a contract length of 8 months the compounding frequency is 1.5 times c.p.a.). Suppose the following bonds are traded in the market on the 15th of August 2013:

• 1-month zero coupon with $1000 face value currently trades for $996.672
• 3-month zero coupon bond with $1000 face value currently trades for $989.555
• 1-year 10% semi-annual coupon bond with $1000 face value currently trades for $1051.706 *
• 1-year 16% quarterly coupon bond with $1000 face value currently trades for $1110.628 **
• 1-year 4% quarterly coupon bond with $1000 face value currently trades for $993.938 **

* x% semi-annual coupon means $1000x%/2 coupon payments every 6 months

** x% quarterly coupon means $1000x%/4 coupon payments every 3 months

What is the value of the FRA for you as a borrower on the 15th of August 2013?

Summary of problem:

This question basically belongs to Finance as well as it explains about calculation of value of the Forward Rate Agreement with the details given.