The price of an FRA is expressed as a forward interest rate. A 3 × 9 FRA is a 180-day loan, 90 days from now. The current annualized 90-day money market rate is 3.5% and the 270-day rate is 4.5%. The actual (unannualized) rates on the 90-day loan (R90) and the 270-day loan (R270) are:
R90 = 0.035 × (90 / 360) = 0.00875
R270 = 0.045 × (270 / 360) = 0.03375
The actual forward rate on a loan with a term of 180 days to be made 90 days from now (written as FR (90, 180)) is:
Annualized = 0.02478 × (360 / 180) = 0.04957 or 4.96%.
