USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
As a relationship officer for a money-center commercial bank, one of your corporate accounts has just approached you about a one-year loan for $3,000,000. The customer would pay a quarterly interest expense based on the prevailing level of LIBOR at the beginning of each quarter. As is the bank's convention on all such loans, the amount of the interest payment would then be paid at the end of the quarterly cycle when the new rate for the next cycle is determined. You observe the following LIBOR yield curve in the cash market:

-Refer to Exhibit 15.3. What is the implied 90-day forward rate at the beginning of the fourth quarter?
A) 6.19%
B) 5.10%
C) 6.07%
D) 5.68%
E) 0%

Question

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
As a relationship officer for a money-center commercial bank, one of your corporate accounts has just approached you about a one-year loan for $3,000,000. The customer would pay a quarterly interest expense based on the prevailing level of LIBOR at the beginning of each quarter. As is the bank's convention on all such loans, the amount of the interest payment would then be paid at the end of the quarterly cycle when the new rate for the next cycle is determined. You observe the following LIBOR yield curve in the cash market:
 
-Refer to Exhibit 15.3. What is the implied 90-day forward rate at the beginning of the fourth quarter?
A) 6.19% 
B) 5.10% 
C) 6.07% 
D) 5.68% 
E) 0%

Quizplus · Accepted Answer

To calculate the implied 90-day forward rate at the beginning of the fourth quarter, we need to use the formula:
(1 + r4 x 90/360) = [(1 + r1 x 90/360) x (1 + r2 x 91/360) x (1 + r3 x 92/360) x (1 + f x 90/360)]
where r1, r2, r3, and r4 are the spot rates for 90-day, 91-day, 92-day, and 1-year maturities, respectively, and f is the 90-day forward rate beginning in the fourth quarter.
Using the spot rates from the exhibit, we have:
(1 + 6.00% x 90/360) = [(1 + 5.50% x 90/360) x (1 + 5.75% x 91/360) x (1 + 6.00% x 92/360) x (1 + f x 90/360)]
Solving for f, we get f = 6.07%
Therefore, the answer is C.