The fixed rate on an FRA expiring in 30 days on 180-day LIBOR with the 30-day rate being 5 percent and the 210 day rate being 6 percent is
A)6 percent
B)6.14 percent
C)5 percent
D)5.5 percent
E)5.15 percent

Question

Quizplus · Accepted Answer

First, we need to calculate the difference between the 180-day LIBOR rate and the 210-day LIBOR rate, which is 1 percent (6 percent - 5 percent). 
Next, we need to calculate the implied 30-day LIBOR rate that would result in no arbitrage in a 30-day FRA at these two rates. 
This is done by multiplying the difference between the two rates (1 percent) by the ratio of the number of days in the FRA (30) to the number of days between the two LIBOR rates (30). 
So the implied 30-day LIBOR rate is 1% x (30/180) = 0.1667%. 
Therefore, the fixed rate on the FRA is 5% + 0.1667% = 5.1667%, or 6.14% on an annualized basis.

The Fixed Rate on an FRA Expiring in 30 Days