Question

The yield curve is flat at 6% per annum. What is the value of an FRA where the holder receives interest at the rate of 8% per annum for a six-month period on a principal of $1,000 starting in two years? All rates are compounded semiannually.

Answer 1

$897.11

Step-by-step explanation:

Interest for six month period =8%/2 =4%=.04.

Given Principal is $1,000.

Given yield curve is 6%. Therefore, semi annual yield =6%/2 =3%.

Interest received for 6 months periods =$1,000 * 4% =$40.

So, the amount that would be received after 2 years and 6 months =$1,000+$40 =$1,040.

To arrive at the value of the forward rate agreement currently, the future value of the FRA needs to be discounted with 3% for a five period interval, because there are five half years to receive the amount of $1,040.

Therefore, present value of FRA =$1,040 /(1+.03)^5

=$897.11