Since we have moved 30 days into the FRA, the new rate for the end of the contract is the 30-day rate (60 days originally minus 30 days passed) and the new rate for the settlement of the loan is the 120-day rate (150 days originally minus 30 days passed).
With that information, the pricing is straightforward:
The actual, unannualized rate on the 30-day loan is:
R30 = 0.022 × 30/360 = 0.00183
The actual, unannualized rate on the 120-day loan is:
R120 = 0.038 × 120/360 = 0.01267
The rate on a 90-day loan to be made 30 days from now is:
FR (30,90) = ((1 + R120) / (1 + R30)) − 1
FR (30,90) = ((1 + 0.01267) / (1 + 0.00183)) − 1
FR (30,90) = (1.01267 / 1.00183) − 1
FR (30,90) = 1.010820 − 1
FR (30,90) = 1.0820%
We annualize this rate using the formula:
1.082% × (360/90) = 4.33%
The interest saving is:
Interest saving = ( (0.0433 × 90/360) − (0.0362 × 90/360) ) × 25,000,000
Interest saving = (0.01083 − 0.00905) × 25,000,000
Interest saving = 0.00178 × 25,000,000
Interest saving = 44,500
The interest “saving” is a positive 44,500. Discounting that back at the current 120-day rate we have:
FRA value = 44,500 / (1 + ( 0.038 × 120/360) )
FRA value = 44,500 / (1 + ( 0.012667) )
FRA value = 44,500 / 1.012667
FRA value = 43,943
The value of the FRA to Vetements Verdun 30 days into the contract is 43,943. In other words, they are due 43,943.