The payoff to the holder of a long FRA on 90-day LIBOR with a fixed rate of 8.75 percent,a notional amount of $20 million if the underlying is 9 percent at expiration is
A)$12,500
B)-$12,500
C)-$12,225
D)$12,225
E)-$48,900

Question

Quizplus · Accepted Answer

The payoff to the holder of a long FRA (Forward Rate Agreement) is calculated as the difference between the agreed fixed rate and the actual rate at expiration, multiplied by the notional amount, and then adjusted for the time period to reflect the actual period of the loan (in this case, 90 days or 0.25 of a year since there are 360 days in the banking year). The formula for the payoff is: $$ \text{Payoff} = \text{Notional Amount} \times (\text{Actual Rate} - \text{Fixed Rate}) \times \frac{\text{Time Period}}{360} $$ Substituting the given values: $$ \text{Payoff} = \$20,000,000 \times (0.09 - 0.0875) \times \frac{90}{360} = \$12,500 $$ However, this amount needs to be discounted back to present value because the payoff is received at the end of the period, not immediately. The discount factor is $$ \frac{1}{1 + \text{Actual Rate} \times \frac{\text{Time Period}}{360}} = \frac{1}{1 + 0.09 \times \frac{90}{360}} $$ Therefore, the present value of the payoff is: $$ \$12,500 \times \frac{1}{1 + 0.09 \times \frac{90}{360}} = \$12,225 $$

The Payoff to the Holder of a Long FRA on 90-Day