A 1x4 FRA is a 90-day loan, 30 days from today.
The actual rate on the 30-day loan is: R30 = 0.05 x 30/360 = 0.004167
The actual rate on the 120-day loan is: R120 = 0.07 x 120/360 = 0.02333
FR (30,90) = [(1+ R120)/(1+ R30)] – 1 = (1.023333/1.004167) – 1 = 0.0190871
The annualized 90-day rate = 0.0190871 x 360/90 = .07634 = 7.63%
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